[{"accepted":true,"classification":"PI","complexity":"A","description":"A very simple linear ODE.","exact_solution":"c0*exp(-par0*t)","id":"ca64ec254097f3b3cbc8489a1a9a4259","ivps":[{"exact_solution":"1.0*exp(-1.0*t)","id":1,"initial_values":"1.0","ode_id":"ca64ec254097f3b3cbc8489a1a9a4259","parameter_values":"1.0"},{"exact_solution":"2.0*exp(-0.5*t)","id":2,"initial_values":"2.0","ode_id":"ca64ec254097f3b3cbc8489a1a9a4259","parameter_values":"0.5"},{"exact_solution":"1.0*exp(-[1.0,2.0]*t)","id":9,"initial_values":"1.0","ode_id":"ca64ec254097f3b3cbc8489a1a9a4259","parameter_values":"[1.0,2.0]"},{"exact_solution":"[0.5,1.5]*exp(-1.5*t)","id":70,"initial_values":"[0.5,1.5]","ode_id":"ca64ec254097f3b3cbc8489a1a9a4259","parameter_values":"1.5"},{"exact_solution":"[0.5,1.5]*exp(-[1,2]*t)","id":71,"initial_values":"[0.5,1.5]","ode_id":"ca64ec254097f3b3cbc8489a1a9a4259","parameter_values":"[1,2]"},{"exact_solution":"-2.0*exp(-(-0.5)*t)","id":81,"initial_values":"-2.0","ode_id":"ca64ec254097f3b3cbc8489a1a9a4259","parameter_values":"-0.5"},{"exact_solution":"[-1.5,-0.5]*exp(-[-2.0,-1.0]*t)","id":82,"initial_values":"[-1.5,-0.5]","ode_id":"ca64ec254097f3b3cbc8489a1a9a4259","parameter_values":"[-2.0,-1.0]"}],"keywords":"min test set","linearity":"L","name":"A1 DETEST","parameter_count":1,"real_problem":false,"right_side":"-par0*x0","variable_count":1},{"accepted":true,"classification":"PI","complexity":"A","description":"A special case of the Riccati equation.","exact_solution":"c0/sqrt((c0**2)*t+1.0)","id":"92703b225d77aa6c1bfc284217aa6069","ivps":[{"exact_solution":"1.0/sqrt((1.0**2)*t+1.0)","id":48,"initial_values":"1.0","ode_id":"92703b225d77aa6c1bfc284217aa6069","parameter_values":""},{"exact_solution":"[0.5,1.5]/sqrt(([0.5,1.5]**2)*t+1.0)","id":49,"initial_values":"[0.5,1.5]","ode_id":"92703b225d77aa6c1bfc284217aa6069","parameter_values":""}],"keywords":"min test set","linearity":"NL","name":"A2 DETEST","parameter_count":0,"real_problem":false,"right_side":"-0.5*x0**3","variable_count":1},{"accepted":true,"classification":"PI","complexity":"A","description":"A simple oscillatory problem; derived from a linear non-autonomous equation with variable coefficients.","exact_solution":"t;c1*exp(sin(t))","id":"7532b05e8b9b1d3171863e6a46a29796","ivps":[{"exact_solution":"t;1.0*exp(sin(t))","id":32,"initial_values":"0.0;1.0","ode_id":"7532b05e8b9b1d3171863e6a46a29796","parameter_values":""},{"exact_solution":"t;[0.9,1.25]*exp(sin(t))","id":33,"initial_values":"0.0;[0.9,1.25]","ode_id":"7532b05e8b9b1d3171863e6a46a29796","parameter_values":""}],"keywords":"non-linear;simple;periodic","linearity":"L","name":"A3 DETEST","parameter_count":0,"real_problem":false,"right_side":"1.0;x1*cos(x0)","variable_count":2},{"accepted":true,"classification":"PI","complexity":"A","description":"A logistic curve.","exact_solution":"20.0/(((20.0-c0)/c0)*exp(-t/4.0)+1.0)","id":"7bd06913e39a7b7cfb6e08858eedf374","ivps":[{"exact_solution":"20.0/(((20.0-1.0)/1.0)*exp(-t/4.0)+1.0)","id":34,"initial_values":"1.0","ode_id":"7bd06913e39a7b7cfb6e08858eedf374","parameter_values":""},{"exact_solution":"20.0/(((20.0-[0.5,1.25])/[0.5,1.25])*exp(-t/4.0)+1.0)","id":35,"initial_values":"[0.5,1.25]","ode_id":"7bd06913e39a7b7cfb6e08858eedf374","parameter_values":""}],"keywords":"","linearity":"NL","name":"A4 DETEST","parameter_count":0,"real_problem":false,"right_side":"x0*(20.0-x0)/80.0","variable_count":1},{"accepted":true,"classification":"PI","complexity":"A","description":"Derived from a non-autonomous equation with trajectories in the form of a spiral curve.","exact_solution":"","id":"79b73890912ff9464fcbeeb39bf59d2e","ivps":[{"exact_solution":"","id":52,"initial_values":"0.0;4.0","ode_id":"79b73890912ff9464fcbeeb39bf59d2e","parameter_values":""},{"exact_solution":"","id":53,"initial_values":"0.0;[4.0,4.25]","ode_id":"79b73890912ff9464fcbeeb39bf59d2e","parameter_values":""}],"keywords":"homogeneous","linearity":"NL","name":"A5 DETEST","parameter_count":0,"real_problem":false,"right_side":"1.0;(x1-x0)/(x1+x0)","variable_count":2},{"accepted":true,"classification":"PI","complexity":"B","description":"The Laub-Loomis model is a seven-dimensional ODE for studying enzymatic activities.","exact_solution":"","id":"e3c5f98a10ae98897a158cef601c101d","ivps":[{"exact_solution":"","id":121,"initial_values":"1.2;1.05;1.5;2.4;1.0;0.1;0.45","ode_id":"e3c5f98a10ae98897a158cef601c101d","parameter_values":""},{"exact_solution":"","id":122,"initial_values":"[1.19,1.21];[1.04,1.06];[1.49,1.51];[2.39,2.41];[0.99,1.01];[0.09,0.11];[0.44,0.46]","ode_id":"e3c5f98a10ae98897a158cef601c101d","parameter_values":""},{"exact_solution":"","id":123,"initial_values":"[1.1,1.3];[0.95,1.15];[1.4,1.6];[2.3,2.5];[0.9,1.1];[0.0,0.2];[0.35,0.55]","ode_id":"e3c5f98a10ae98897a158cef601c101d","parameter_values":""}],"keywords":"","linearity":"NL","name":"ARCH Benchmark 1","parameter_count":0,"real_problem":false,"right_side":"1.4*x2-0.9*x0;2.5*x4-1.5*x1;0.6*x6-0.8*x1*x2;2.0-1.3*x2*x3;0.7*x0-x3*x4;0.3*x0-3.1*x5;1.8*x5-1.5*x1*x6","variable_count":7},{"accepted":true,"classification":"PI","complexity":"B","description":"The growth of two conflicting populations.","exact_solution":"","id":"dac0ae095d80eb999fbf63159185e84d","ivps":[{"exact_solution":"","id":12,"initial_values":"1.0;3.0","ode_id":"dac0ae095d80eb999fbf63159185e84d","parameter_values":""},{"exact_solution":"","id":13,"initial_values":"[0.9,1.1];3.0","ode_id":"dac0ae095d80eb999fbf63159185e84d","parameter_values":""}],"keywords":"min test set","linearity":"NL","name":"B1 DETEST","parameter_count":0,"real_problem":false,"right_side":"2.0*x0-2.0*x0*x1;-x1+x0*x1","variable_count":2},{"accepted":true,"classification":"PI","complexity":"B","description":"A linear chemical reaction.","exact_solution":"(c0+c1)*exp(-t)+(c2-c0)*exp(-t)*(-1.0+t)+(c2-c1-c0)*exp(-2.0*t);(c2-c0)*exp(-t)-(c2-c1-c0)*exp(-2.0*t);(c0+c1)*exp(-t)+(c2-c0)*exp(-t)*t+(c2-c1-c0)*exp(-2.0*t)","id":"fa9b7358e602537f4f77a08ff5479200","ivps":[{"exact_solution":"(2.0+0.0)*exp(-t)+(1.0-2.0)*exp(-t)*(-1.0+t)+(1.0-0.0-2.0)*exp(-2.0*t);(1.0-2.0)*exp(-t)-(1.0-0.0-2.0)*exp(-2.0*t);(2.0+0.0)*exp(-t)+(1.0-2.0)*exp(-t)*t+(1.0-0.0-2.0)*exp(-2.0*t)","id":10,"initial_values":"2.0;0.0;1.0","ode_id":"fa9b7358e602537f4f77a08ff5479200","parameter_values":""},{"exact_solution":"([1.5,2.5]+0.0)*exp(-t)+(1.0-[1.5,2.5])*exp(-t)*(-1.0+t)+(1.0-0.0-[1.5,2.5])*exp(-2.0*t);(1.0-[1.5,2.5])*exp(-t)-(1.0-0.0-[1.5,2.5])*exp(-2.0*t);([1.5,2.5]+0.0)*exp(-t)+(1.0-[1.5,2.5])*exp(-t)*t+(1.0-0.0-[1.5,2.5])*exp(-2.0*t)","id":11,"initial_values":"[1.5,2.5];0.0;1.0","ode_id":"fa9b7358e602537f4f77a08ff5479200","parameter_values":""}],"keywords":"min test set","linearity":"L","name":"B2 DETEST","parameter_count":0,"real_problem":false,"right_side":"-x0+x1;-x0-2.0*x1+x2;x1-x2","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"A nonlinear chemical reaction.","exact_solution":"","id":"89f9da817447af706fb190596e6dcf48","ivps":[{"exact_solution":"","id":54,"initial_values":"1.0;0.0;0.0","ode_id":"89f9da817447af706fb190596e6dcf48","parameter_values":""},{"exact_solution":"","id":55,"initial_values":"[1.0,1.25];0.0;0.0","ode_id":"89f9da817447af706fb190596e6dcf48","parameter_values":""}],"keywords":"non-linear;uncoupled","linearity":"NL","name":"B3 DETEST","parameter_count":0,"real_problem":false,"right_side":"-x0;x0-x1**2;x1**2","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"The integral surface of a torus.","exact_solution":"","id":"c7572c25f9ee6407b75b4c150db3fec1","ivps":[{"exact_solution":"","id":56,"initial_values":"3.0;0.0;0.0","ode_id":"c7572c25f9ee6407b75b4c150db3fec1","parameter_values":""},{"exact_solution":"","id":57,"initial_values":"[3.0,3.25];0.0;0.0","ode_id":"c7572c25f9ee6407b75b4c150db3fec1","parameter_values":""}],"keywords":"","linearity":"NL","name":"B4 DETEST","parameter_count":0,"real_problem":false,"right_side":"-x1-x0*x2/sqrt(x0**2+x1**2);x0-x1*x2/sqrt(x0**2+x1**2);x0/sqrt(x0**2+x1**2)","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"Euler equations of motion for a rigid body without external forces.","exact_solution":"","id":"2f7364cf78669a9aa5b120ee181b09cd","ivps":[{"exact_solution":"","id":36,"initial_values":"0.0;1.0;1.0","ode_id":"2f7364cf78669a9aa5b120ee181b09cd","parameter_values":""},{"exact_solution":"","id":37,"initial_values":"0.0;[1.0,1.25];[0.9,1.1]","ode_id":"2f7364cf78669a9aa5b120ee181b09cd","parameter_values":""}],"keywords":"non-linear;motion","linearity":"NL","name":"B5 DETEST","parameter_count":0,"real_problem":false,"right_side":"x1*x2;-x0*x2;-0.51*x0*x1","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"A linear system with constant coefficients.","exact_solution":"(3.0*c0-2.0*c1)*exp(-t)+2.0*(c1-c0)*exp(-2.0*t);(3.0*c0-2.0*c1)*exp(-t)+3.0*(c1-c0)*exp(-2.0*t)","id":"359ee05d7d37e69d492ed6e46e671f43","ivps":[{"exact_solution":"(3.0*[0.5,1.5]-2.0*[-1.5,-0.5])*exp(-t)+2.0*([-1.5,-0.5]-[0.5,1.5])*exp(-2.0*t);(3.0*[0.5,1.5]-2.0*[-1.5,-0.5])*exp(-t)+3.0*([-1.5,-0.5]-[0.5,1.5])*exp(-2.0*t)","id":26,"initial_values":"[0.5,1.5];[-1.5,-0.5]","ode_id":"359ee05d7d37e69d492ed6e46e671f43","parameter_values":""},{"exact_solution":"(3.0*1.0-2.0*(-1.0))*exp(-t)+2.0*(-1.0-1.0)*exp(-2.0*t);(3.0*1.0-2.0*(-1.0))*exp(-t)+3.0*(-1.0-1.0)*exp(-2.0*t)","id":27,"initial_values":"1.0;-1.0","ode_id":"359ee05d7d37e69d492ed6e46e671f43","parameter_values":""},{"exact_solution":"(3.0*[1.5,2.0]-2.0*[-2.0,-1.5])*exp(-t)+2.0*([-2.0,-1.5]-[1.5,2.0])*exp(-2.0*t);(3.0*[1.5,2.0]-2.0*[-2.0,-1.5])*exp(-t)+3.0*([-2.0,-1.5]-[1.5,2.0])*exp(-2.0*t)","id":83,"initial_values":"[1.5,2.0];[-2.0,-1.5]","ode_id":"359ee05d7d37e69d492ed6e46e671f43","parameter_values":""}],"keywords":"","linearity":"L","name":"Bachman's Example","parameter_count":0,"real_problem":false,"right_side":"x0-2.0*x1;3.0*x0-4.0*x1","variable_count":2},{"accepted":true,"classification":"PI","complexity":"B","description":"A radioactive decay chain with all constants equal to 1. Please note that the supplied exact solution is correct only for certain  initial conditions (e.g., those from the IVPs).","exact_solution":"c0*exp(-t);c0*t*exp(-t);c0*((t)**2/2.0)*exp(-t);c0*((t)**3/6.0)*exp(-t);c0*((t)**4/24.0)*exp(-t);c0*((t)**5/120.0)*exp(-t);c0*((t)**6/720.0)*exp(-t);c0*((t)**7/5040.0)*exp(-t);c0*((t)**8/40320.0)*exp(-t);-(c0*exp(-t)*((t)**8+8.0*(t)**7+56.0*(t)**6+336.0*(t)**5+1680.0*((t)**2)**2+6720.0*(t)**3+20160.0*(t)**2+40320.0*t+40320.0))/40320.0+c0","id":"e0a1c2249d57d7ee867917c66002949f","ivps":[{"exact_solution":"1.0*exp(-t);1.0*t*exp(-t);1.0*((t)**2/2.0)*exp(-t);1.0*((t)**3/6.0)*exp(-t);1.0*((t)**4/24.0)*exp(-t);1.0*((t)**5/120.0)*exp(-t);1.0*((t)**6/720.0)*exp(-t);1.0*((t)**7/5040.0)*exp(-t);1.0*((t)**8/40320.0)*exp(-t);-(1.0*exp(-t)*((t)**8+8.0*(t)**7+56.0*(t)**6+336.0*(t)**5+1680.0*((t)**2)**2+6720.0*(t)**3+20160.0*(t)**2+40320.0*t+40320.0))/40320.0+1.0","id":58,"initial_values":"1.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0","ode_id":"e0a1c2249d57d7ee867917c66002949f","parameter_values":""},{"exact_solution":"[0.5,1.5]*exp(-t);[0.5,1.5]*t*exp(-t);[0.5,1.5]*((t)**2/2.0)*exp(-t);[0.5,1.5]*((t)**3/6.0)*exp(-t);[0.5,1.5]*((t)**4/24.0)*exp(-t);[0.5,1.5]*((t)**5/120.0)*exp(-t);[0.5,1.5]*((t)**6/720.0)*exp(-t);[0.5,1.5]*((t)**7/5040.0)*exp(-t);[0.5,1.5]*((t)**8/40320.0)*exp(-t);-([0.5,1.5]*exp(-t)*((t)**8+8.0*(t)**7+56.0*(t)**6+336.0*(t)**5+1680.0*((t)**2)**2+6720.0*(t)**3+20160.0*(t)**2+40320.0*t+40320.0))/40320.0+[0.5,1.5]","id":59,"initial_values":"[0.5,1.5];0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0","ode_id":"e0a1c2249d57d7ee867917c66002949f","parameter_values":""}],"keywords":"decoupled","linearity":"L","name":"C1 DETEST","parameter_count":0,"real_problem":false,"right_side":"-x0;x0-x1;x1-x2;x2-x3;x3-x4;x4-x5;x5-x6;x6-x7;x7-x8;x8","variable_count":10},{"accepted":true,"classification":"PI","complexity":"B","description":"A radioactive decay chain; Bateman's equation with different decay constants. Please note that the supplied exact solution is correct only for certain  initial conditions (e.g., those from the IVPs).","exact_solution":"c0*exp(-t);c0*(exp(-t)-exp(-2.0*t));c0*(exp(-t)-2.0*exp(-2.0*t)+exp(-3.0*t));c0*(exp(-t)-3.0*exp(-2.0*t)+3.0*exp(-3.0*t)-exp(-4.0*t));c0*(exp(-t)-4.0*exp(-2.0*t)+6.0*exp(-3.0*t)-4.0*exp(-4.0*t)+exp(-5.0*t));c0*(exp(-t)-5.0*exp(-2.0*t)+10.0*exp(-3.0*t)-10.0*exp(-4.0*t)+5.0*exp(-5.0*t)-exp(-6.0*t));c0*(exp(-t)-6.0*exp(-2.0*t)+15.0*exp(-3.0*t)-20.0*exp(-4.0*t)+15.0*exp(-5.0*t)-6.0*exp(-6.0*t)+exp(-7.0*t));c0*(exp(-t)-7.0*exp(-2.0*t)+21.0*exp(-3.0*t)-35.0*exp(-4.0*t)+35.0*exp(-5.0*t)-21.0*exp(-6.0*t)+7.0*exp(-7.0*t)-exp(-8.0*t));c0*(exp(-t)-8.0*exp(-2.0*t)+28.0*exp(-3.0*t)-56.0*exp(-4.0*t)+70.0*exp(-5.0*t)-56.0*exp(-6.0*t)+28.0*exp(-7.0*t)-8.0*exp(-8.0*t)+exp(-9.0*t));c0*(-9.0*exp(-t)+36.0*exp(-2.0*t)-84.0*exp(-3.0*t)+126.0*exp(-4.0*t)-126.0*exp(-5.0*t)+84.0*exp(-6.0*t)-36.0*exp(-7.0*t)+9.0*exp(-8.0*t)-exp(-9.0*t))+c0","id":"fa585020ce008eade0c87a316f7c1dae","ivps":[{"exact_solution":"1.0*exp(-t);1.0*(exp(-t)-exp(-2.0*t));1.0*(exp(-t)-2.0*exp(-2.0*t)+exp(-3.0*t));1.0*(exp(-t)-3.0*exp(-2.0*t)+3.0*exp(-3.0*t)-exp(-4.0*t));1.0*(exp(-t)-4.0*exp(-2.0*t)+6.0*exp(-3.0*t)-4.0*exp(-4.0*t)+exp(-5.0*t));1.0*(exp(-t)-5.0*exp(-2.0*t)+10.0*exp(-3.0*t)-10.0*exp(-4.0*t)+5.0*exp(-5.0*t)-exp(-6.0*t));1.0*(exp(-t)-6.0*exp(-2.0*t)+15.0*exp(-3.0*t)-20.0*exp(-4.0*t)+15.0*exp(-5.0*t)-6.0*exp(-6.0*t)+exp(-7.0*t));1.0*(exp(-t)-7.0*exp(-2.0*t)+21.0*exp(-3.0*t)-35.0*exp(-4.0*t)+35.0*exp(-5.0*t)-21.0*exp(-6.0*t)+7.0*exp(-7.0*t)-exp(-8.0*t));1.0*(exp(-t)-8.0*exp(-2.0*t)+28.0*exp(-3.0*t)-56.0*exp(-4.0*t)+70.0*exp(-5.0*t)-56.0*exp(-6.0*t)+28.0*exp(-7.0*t)-8.0*exp(-8.0*t)+exp(-9.0*t));1.0*(-9.0*exp(-t)+36.0*exp(-2.0*t)-84.0*exp(-3.0*t)+126.0*exp(-4.0*t)-126.0*exp(-5.0*t)+84.0*exp(-6.0*t)-36.0*exp(-7.0*t)+9.0*exp(-8.0*t)-exp(-9.0*t))+1.0","id":60,"initial_values":"1.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0","ode_id":"fa585020ce008eade0c87a316f7c1dae","parameter_values":""},{"exact_solution":"[0.9,1.1]*exp(-t);[0.9,1.1]*(exp(-t)-exp(-2.0*t));[0.9,1.1]*(exp(-t)-2.0*exp(-2.0*t)+exp(-3.0*t));[0.9,1.1]*(exp(-t)-3.0*exp(-2.0*t)+3.0*exp(-3.0*t)-exp(-4.0*t));[0.9,1.1]*(exp(-t)-4.0*exp(-2.0*t)+6.0*exp(-3.0*t)-4.0*exp(-4.0*t)+exp(-5.0*t));[0.9,1.1]*(exp(-t)-5.0*exp(-2.0*t)+10.0*exp(-3.0*t)-10.0*exp(-4.0*t)+5.0*exp(-5.0*t)-exp(-6.0*t));[0.9,1.1]*(exp(-t)-6.0*exp(-2.0*t)+15.0*exp(-3.0*t)-20.0*exp(-4.0*t)+15.0*exp(-5.0*t)-6.0*exp(-6.0*t)+exp(-7.0*t));[0.9,1.1]*(exp(-t)-7.0*exp(-2.0*t)+21.0*exp(-3.0*t)-35.0*exp(-4.0*t)+35.0*exp(-5.0*t)-21.0*exp(-6.0*t)+7.0*exp(-7.0*t)-exp(-8.0*t));[0.9,1.1]*(exp(-t)-8.0*exp(-2.0*t)+28.0*exp(-3.0*t)-56.0*exp(-4.0*t)+70.0*exp(-5.0*t)-56.0*exp(-6.0*t)+28.0*exp(-7.0*t)-8.0*exp(-8.0*t)+exp(-9.0*t));[0.9,1.1]*(-9.0*exp(-t)+36.0*exp(-2.0*t)-84.0*exp(-3.0*t)+126.0*exp(-4.0*t)-126.0*exp(-5.0*t)+84.0*exp(-6.0*t)-36.0*exp(-7.0*t)+9.0*exp(-8.0*t)-exp(-9.0*t))+[0.9,1.1]","id":61,"initial_values":"[0.9,1.1];0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0","ode_id":"fa585020ce008eade0c87a316f7c1dae","parameter_values":""}],"keywords":"decoupled","linearity":"L","name":"C2 DETEST","parameter_count":0,"real_problem":false,"right_side":"-x0;x0-2.0*x1;2.0*x1-3.0*x2;3.0*x2-4.0*x3;4.0*x3-5.0*x4;5.0*x4-6.0*x5;6.0*x5-7.0*x6;7.0*x6-8.0*x7;8.0*x7-9.0*x8;9.0*x8","variable_count":10},{"accepted":true,"classification":"PI","complexity":"B","description":"Derived from a parabolic partial differential equation; n=10","exact_solution":"","id":"8ae842dfbb98f819cad50d0a0811e52d","ivps":[{"exact_solution":"","id":38,"initial_values":"1.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0","ode_id":"8ae842dfbb98f819cad50d0a0811e52d","parameter_values":""},{"exact_solution":"","id":39,"initial_values":"[0.75,1.25];0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0","ode_id":"8ae842dfbb98f819cad50d0a0811e52d","parameter_values":""}],"keywords":"","linearity":"L","name":"C3 DETEST","parameter_count":0,"real_problem":false,"right_side":"-2.0*x0+x1;x0-2.0*x1+x2;x1-2.0*x2+x3;x2-2.0*x3+x4;x3-2.0*x4+x5;x4-2.0*x5+x6;x5-2.0*x6+x7;x6-2.0*x7+x8;x7-2.0*x8+x9;x8-2.0*x9","variable_count":10},{"accepted":true,"classification":"PI","complexity":"C","description":"Derived from a parabolic partial differential equation; n=51.","exact_solution":"","id":"e33f5d4093db669f70be2be2a21184e8","ivps":[{"exact_solution":"","id":15,"initial_values":"[0.5,1.5];0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0","ode_id":"e33f5d4093db669f70be2be2a21184e8","parameter_values":""},{"exact_solution":"","id":84,"initial_values":"1.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0","ode_id":"e33f5d4093db669f70be2be2a21184e8","parameter_values":""}],"keywords":"min test set","linearity":"L","name":"C4 DETEST","parameter_count":0,"real_problem":false,"right_side":"-2.0*x0+x1;x0-2.0*x1+x2;x1-2.0*x2+x3;x2-2.0*x3+x4;x3-2.0*x4+x5;x4-2.0*x5+x6;x5-2.0*x6+x7;x6-2.0*x7+x8;x7-2.0*x8+x9;x8-2.0*x9+x10;x9-2.0*x10+x11;x10-2.0*x11+x12;x11-2.0*x12+x13;x12-2.0*x13+x14;x13-2.0*x14+x15;x14-2.0*x15+x16;x15-2.0*x16+x17;x16-2.0*x17+x18;x17-2.0*x18+x19;x18-2.0*x19+x20;x19-2.0*x20+x21;x20-2.0*x21+x22;x21-2.0*x22+x23;x22-2.0*x23+x24;x23-2.0*x24+x25;x24-2.0*x25+x26;x25-2.0*x26+x27;x26-2.0*x27+x28;x27-2.0*x28+x29;x28-2.0*x29+x30;x29-2.0*x30+x31;x30-2.0*x31+x32;x31-2.0*x32+x33;x32-2.0*x33+x34;x33-2.0*x34+x35;x34-2.0*x35+x36;x35-2.0*x36+x37;x36-2.0*x37+x38;x37-2.0*x38+x39;x38-2.0*x39+x40;x39-2.0*x40+x41;x40-2.0*x41+x42;x41-2.0*x42+x43;x42-2.0*x43+x44;x43-2.0*x44+x45;x44-2.0*x45+x46;x45-2.0*x46+x47;x46-2.0*x47+x48;x47-2.0*x48+x49;x48-2.0*x49+x50;x49-2.0*x50","variable_count":51},{"accepted":true,"classification":"PI","complexity":"C","description":"Derived from the five body problem: the motion of 5 outer planets about the sun.","exact_solution":"","id":"b44cfc8ff349d187930aaf2582358393","ivps":[{"exact_solution":"","id":116,"initial_values":"3.4294741518;-0.5571605704;6.6414554255;-0.4155707763;11.2630437207;-0.3253256691;-30.1552268759;-0.0240476254;-21.1238353380;-0.1768607531;3.3538695971;0.5056967832;5.9715695787;0.3656827228;14.6952576794;0.1897060219;1.6569996640;-0.2876595326;28.4465098142;-0.2163934530;1.3549401715;0.2305785439;2.1823149972;0.1691432132;6.2796052506;0.0877265322;1.4378575272;-0.1172195431;15.3882659679;-0.0148647893","ode_id":"b44cfc8ff349d187930aaf2582358393","parameter_values":""},{"exact_solution":"","id":132,"initial_values":"[3.4194741518,3.4394741518];-0.5571605704;6.6414554255;-0.4155707763;11.2630437207;-0.3253256691;-30.1552268759;-0.0240476254;-21.1238353380;-0.1768607531;3.3538695971;0.5056967832;5.9715695787;0.3656827228;14.6952576794;0.1897060219;1.6569996640;-0.2876595326;28.4465098142;-0.2163934530;1.3549401715;0.2305785439;2.1823149972;0.1691432132;6.2796052506;0.0877265322;1.4378575272;-0.1172195431;15.3882659679;-0.0148647893","ode_id":"b44cfc8ff349d187930aaf2582358393","parameter_values":""}],"keywords":"chaotic;min test set","linearity":"NL","name":"C5 DETEST","parameter_count":0,"real_problem":false,"right_side":"x1;(-1.00096076292*x0/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2))+0.00028558373*((x2-x0)/(((x2-x0)**2+(x12-x10)**2+(x22-x20)**2)*sqrt((x2-x0)**2+(x12-x10)**2+(x22-x20)**2))-x2/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+4.372731e-05*((x4-x0)/(((x4-x0)**2+(x14-x10)**2+(x24-x20)**2)*sqrt((x4-x0)**2+(x14-x10)**2+(x24-x20)**2))-x4/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+5.177591e-05*((x6-x0)/(((x6-x0)**2+(x16-x10)**2+(x26-x20)**2)*sqrt((x6-x0)**2+(x16-x10)**2+(x26-x20)**2))-x6/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2)))+2.77777e-06*((x8-x0)/(((x8-x0)**2+(x18-x10)**2+(x28-x20)**2)*sqrt((x8-x0)**2+(x18-x10)**2+(x28-x20)**2))-x8/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x3;(-1.00029156055*x2/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2))+0.0009547861*((x0-x2)/(((x0-x2)**2+(x10-x12)**2+(x20-x22)**2)*sqrt((x0-x2)**2+(x10-x12)**2+(x20-x22)**2))-x0/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+4.372731e-05*((x4-x2)/(((x4-x2)**2+(x14-x12)**2+(x24-x22)**2)*sqrt((x4-x2)**2+(x14-x12)**2+(x24-x22)**2))-x4/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+5.177591e-05*((x6-x2)/(((x6-x2)**2+(x16-x12)**2+(x26-x22)**2)*sqrt((x6-x2)**2+(x16-x12)**2+(x26-x22)**2))-x6/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2)))+2.77777e-06*((x8-x2)/(((x8-x2)**2+(x18-x12)**2+(x28-x22)**2)*sqrt((x8-x2)**2+(x18-x12)**2+(x28-x22)**2))-x8/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x5;(-1.00004970413*x4/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2))+0.0009547861*((x0-x4)/(((x0-x4)**2+(x10-x14)**2+(x20-x24)**2)*sqrt((x0-x4)**2+(x10-x14)**2+(x20-x24)**2))-x0/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+0.00028558373*((x2-x4)/(((x2-x4)**2+(x12-x14)**2+(x22-x24)**2)*sqrt((x2-x4)**2+(x12-x14)**2+(x22-x24)**2))-x2/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+5.177591e-05*((x6-x4)/(((x6-x4)**2+(x16-x14)**2+(x26-x24)**2)*sqrt((x6-x4)**2+(x16-x14)**2+(x26-x24)**2))-x6/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2)))+2.77777e-06*((x8-x4)/(((x8-x4)**2+(x18-x14)**2+(x28-x24)**2)*sqrt((x8-x4)**2+(x18-x14)**2+(x28-x24)**2))-x8/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x7;(-1.00005775273*x6/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2))+0.0009547861*((x0-x6)/(((x0-x6)**2+(x10-x16)**2+(x20-x26)**2)*sqrt((x0-x6)**2+(x10-x16)**2+(x20-x26)**2))-x0/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+0.00028558373*((x2-x6)/(((x2-x6)**2+(x12-x16)**2+(x22-x26)**2)*sqrt((x2-x6)**2+(x12-x16)**2+(x22-x26)**2))-x2/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+4.372731e-05*((x4-x6)/(((x4-x6)**2+(x14-x16)**2+(x24-x26)**2)*sqrt((x4-x6)**2+(x14-x16)**2+(x24-x26)**2))-x4/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+2.77777e-06*((x8-x6)/(((x8-x6)**2+(x18-x16)**2+(x28-x26)**2)*sqrt((x8-x6)**2+(x18-x16)**2+(x28-x26)**2))-x8/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x9;(-1.00000875459*x8/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))+0.0009547861*((x0-x8)/(((x0-x8)**2+(x10-x18)**2+(x20-x28)**2)*sqrt((x0-x8)**2+(x10-x18)**2+(x20-x28)**2))-x0/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+0.00028558373*((x2-x8)/(((x2-x8)**2+(x12-x18)**2+(x22-x28)**2)*sqrt((x2-x8)**2+(x12-x18)**2+(x22-x28)**2))-x2/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+4.372731e-05*((x4-x8)/(((x4-x8)**2+(x14-x18)**2+(x24-x28)**2)*sqrt((x4-x8)**2+(x14-x18)**2+(x24-x28)**2))-x4/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+5.177591e-05*((x6-x8)/(((x6-x8)**2+(x16-x18)**2+(x26-x28)**2)*sqrt((x6-x8)**2+(x16-x18)**2+(x26-x28)**2))-x6/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2))));x11;(-1.00096076292*x10/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2))+0.00028558373*((x12-x10)/(((x2-x0)**2+(x12-x10)**2+(x22-x20)**2)*sqrt((x2-x0)**2+(x12-x10)**2+(x22-x20)**2))-x12/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+4.372731e-05*((x14-x10)/(((x4-x0)**2+(x14-x10)**2+(x24-x20)**2)*sqrt((x4-x0)**2+(x14-x10)**2+(x24-x20)**2))-x14/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+5.177591e-05*((x16-x10)/(((x6-x0)**2+(x16-x10)**2+(x26-x20)**2)*sqrt((x6-x0)**2+(x16-x10)**2+(x26-x20)**2))-x16/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2)))+2.77777e-06*((x18-x10)/(((x8-x0)**2+(x18-x10)**2+(x28-x20)**2)*sqrt((x8-x0)**2+(x18-x10)**2+(x28-x20)**2))-x18/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x13;(-1.00029156055*x12/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2))+0.0009547861*((x10-x12)/(((x0-x2)**2+(x10-x12)**2+(x20-x22)**2)*sqrt((x0-x2)**2+(x10-x12)**2+(x20-x22)**2))-x10/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+4.372731e-05*((x14-x12)/(((x4-x2)**2+(x14-x12)**2+(x24-x22)**2)*sqrt((x4-x2)**2+(x14-x12)**2+(x24-x22)**2))-x14/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+5.177591e-05*((x16-x12)/(((x6-x2)**2+(x16-x12)**2+(x26-x22)**2)*sqrt((x6-x2)**2+(x16-x12)**2+(x26-x22)**2))-x16/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2)))+2.77777e-06*((x18-x12)/(((x8-x2)**2+(x18-x12)**2+(x28-x22)**2)*sqrt((x8-x2)**2+(x18-x12)**2+(x28-x22)**2))-x18/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x15;(-1.00004970413*x14/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2))+0.0009547861*((x10-x14)/(((x0-x4)**2+(x10-x14)**2+(x20-x24)**2)*sqrt((x0-x4)**2+(x10-x14)**2+(x20-x24)**2))-x10/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+0.00028558373*((x12-x14)/(((x2-x4)**2+(x12-x14)**2+(x22-x24)**2)*sqrt((x2-x4)**2+(x12-x14)**2+(x22-x24)**2))-x12/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+5.177591e-05*((x16-x14)/(((x6-x4)**2+(x16-x14)**2+(x26-x24)**2)*sqrt((x6-x4)**2+(x16-x14)**2+(x26-x24)**2))-x16/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2)))+2.77777e-06*((x18-x14)/(((x8-x4)**2+(x18-x14)**2+(x28-x24)**2)*sqrt((x8-x4)**2+(x18-x14)**2+(x28-x24)**2))-x18/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x17;(-1.00005775273*x16/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2))+0.0009547861*((x10-x16)/(((x0-x6)**2+(x10-x16)**2+(x20-x26)**2)*sqrt((x0-x6)**2+(x10-x16)**2+(x20-x26)**2))-x10/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+0.00028558373*((x12-x16)/(((x2-x6)**2+(x12-x16)**2+(x22-x26)**2)*sqrt((x2-x6)**2+(x12-x16)**2+(x22-x26)**2))-x12/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+4.372731e-05*((x14-x16)/(((x4-x6)**2+(x14-x16)**2+(x24-x26)**2)*sqrt((x4-x6)**2+(x14-x16)**2+(x24-x26)**2))-x14/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+2.77777e-06*((x18-x16)/(((x8-x6)**2+(x18-x16)**2+(x28-x26)**2)*sqrt((x8-x6)**2+(x18-x16)**2+(x28-x26)**2))-x18/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x19;(-1.00000875459*x18/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))+0.0009547861*((x10-x18)/(((x0-x8)**2+(x10-x18)**2+(x20-x28)**2)*sqrt((x0-x8)**2+(x10-x18)**2+(x20-x28)**2))-x10/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+0.00028558373*((x12-x18)/(((x2-x8)**2+(x12-x18)**2+(x22-x28)**2)*sqrt((x2-x8)**2+(x12-x18)**2+(x22-x28)**2))-x12/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+4.372731e-05*((x14-x18)/(((x4-x8)**2+(x14-x18)**2+(x24-x28)**2)*sqrt((x4-x8)**2+(x14-x18)**2+(x24-x28)**2))-x14/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+5.177591e-05*((x16-x18)/(((x6-x8)**2+(x16-x18)**2+(x26-x28)**2)*sqrt((x6-x8)**2+(x16-x18)**2+(x26-x28)**2))-x16/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2))));x21;(-1.00096076292*x20/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2))+0.00028558373*((x22-x20)/(((x2-x0)**2+(x12-x10)**2+(x22-x20)**2)*sqrt((x2-x0)**2+(x12-x10)**2+(x22-x20)**2))-x22/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+4.372731e-05*((x24-x20)/(((x4-x0)**2+(x14-x10)**2+(x24-x20)**2)*sqrt((x4-x0)**2+(x14-x10)**2+(x24-x20)**2))-x24/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+5.177591e-05*((x26-x20)/(((x6-x0)**2+(x16-x10)**2+(x26-x20)**2)*sqrt((x6-x0)**2+(x16-x10)**2+(x26-x20)**2))-x26/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2)))+2.77777e-06*((x28-x20)/(((x8-x0)**2+(x18-x10)**2+(x28-x20)**2)*sqrt((x8-x0)**2+(x18-x10)**2+(x28-x20)**2))-x28/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x23;(-1.00029156055*x22/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2))+0.0009547861*((x20-x22)/(((x0-x2)**2+(x10-x12)**2+(x20-x22)**2)*sqrt((x0-x2)**2+(x10-x12)**2+(x20-x22)**2))-x20/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+4.372731e-05*((x24-x22)/(((x4-x2)**2+(x14-x12)**2+(x24-x22)**2)*sqrt((x4-x2)**2+(x14-x12)**2+(x24-x22)**2))-x24/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+5.177591e-05*((x26-x22)/(((x6-x2)**2+(x16-x12)**2+(x26-x22)**2)*sqrt((x6-x2)**2+(x16-x12)**2+(x26-x22)**2))-x26/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2)))+2.77777e-06*((x28-x22)/(((x8-x2)**2+(x18-x12)**2+(x28-x22)**2)*sqrt((x8-x2)**2+(x18-x12)**2+(x28-x22)**2))-x28/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x25;(-1.00004970413*x24/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2))+0.0009547861*((x20-x24)/(((x0-x4)**2+(x10-x14)**2+(x20-x24)**2)*sqrt((x0-x4)**2+(x10-x14)**2+(x20-x24)**2))-x20/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+0.00028558373*((x22-x24)/(((x2-x4)**2+(x12-x14)**2+(x22-x24)**2)*sqrt((x2-x4)**2+(x12-x14)**2+(x22-x24)**2))-x22/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+5.177591e-05*((x26-x24)/(((x6-x4)**2+(x16-x14)**2+(x26-x24)**2)*sqrt((x6-x4)**2+(x16-x14)**2+(x26-x24)**2))-x26/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2)))+2.77777e-06*((x28-x24)/(((x8-x4)**2+(x18-x14)**2+(x28-x24)**2)*sqrt((x8-x4)**2+(x18-x14)**2+(x28-x24)**2))-x28/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x27;(-1.00005775273*x26/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2))+0.0009547861*((x20-x26)/(((x0-x6)**2+(x10-x16)**2+(x20-x26)**2)*sqrt((x0-x6)**2+(x10-x16)**2+(x20-x26)**2))-x20/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+0.00028558373*((x22-x26)/(((x2-x6)**2+(x12-x16)**2+(x22-x26)**2)*sqrt((x2-x6)**2+(x12-x16)**2+(x22-x26)**2))-x22/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+4.372731e-05*((x24-x26)/(((x4-x6)**2+(x14-x16)**2+(x24-x26)**2)*sqrt((x4-x6)**2+(x14-x16)**2+(x24-x26)**2))-x24/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+2.77777e-06*((x28-x26)/(((x8-x6)**2+(x18-x16)**2+(x28-x26)**2)*sqrt((x8-x6)**2+(x18-x16)**2+(x28-x26)**2))-x28/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))));x29;(-1.00000875459*x28/(((x8)**2+(x18)**2+(x28)**2)*sqrt((x8)**2+(x18)**2+(x28)**2))+0.0009547861*((x20-x28)/(((x0-x8)**2+(x10-x18)**2+(x20-x28)**2)*sqrt((x0-x8)**2+(x10-x18)**2+(x20-x28)**2))-x20/(((x0)**2+(x10)**2+(x20)**2)*sqrt((x0)**2+(x10)**2+(x20)**2)))+0.00028558373*((x22-x28)/(((x2-x8)**2+(x12-x18)**2+(x22-x28)**2)*sqrt((x2-x8)**2+(x12-x18)**2+(x22-x28)**2))-x22/(((x2)**2+(x12)**2+(x22)**2)*sqrt((x2)**2+(x12)**2+(x22)**2)))+4.372731e-05*((x24-x28)/(((x4-x8)**2+(x14-x18)**2+(x24-x28)**2)*sqrt((x4-x8)**2+(x14-x18)**2+(x24-x28)**2))-x24/(((x4)**2+(x14)**2+(x24)**2)*sqrt((x4)**2+(x14)**2+(x24)**2)))+5.177591e-05*((x26-x28)/(((x6-x8)**2+(x16-x18)**2+(x26-x28)**2)*sqrt((x6-x8)**2+(x16-x18)**2+(x26-x28)**2))-x26/(((x6)**2+(x16)**2+(x26)**2)*sqrt((x6)**2+(x16)**2+(x26)**2))))","variable_count":30},{"accepted":true,"classification":"PI","complexity":"B","description":"Orbit equations.","exact_solution":"","id":"50b60b059fe3c06580c1632802cfc1f9","ivps":[{"exact_solution":"","id":62,"initial_values":"0.5;0.0;0.0;1.7320508075688772","ode_id":"50b60b059fe3c06580c1632802cfc1f9","parameter_values":""},{"exact_solution":"","id":63,"initial_values":"[0.1,0.3];0.0;0.0;[1.22221,1.85715]","ode_id":"50b60b059fe3c06580c1632802cfc1f9","parameter_values":""},{"exact_solution":"","id":86,"initial_values":"[0.45,0.55];0.0;0.0;[1.6236882817719773,1.8559214542766742]","ode_id":"50b60b059fe3c06580c1632802cfc1f9","parameter_values":""},{"exact_solution":"","id":87,"initial_values":"[0.69,0.71];0.0;0.0;[1.3479248526719523,1.3778790674938355]","ode_id":"50b60b059fe3c06580c1632802cfc1f9","parameter_values":""},{"exact_solution":"","id":88,"initial_values":"[0.25,0.35];0.0;0.0;[2.1712405933672376,2.6457513110645907]","ode_id":"50b60b059fe3c06580c1632802cfc1f9","parameter_values":""},{"exact_solution":"","id":89,"initial_values":"[0.09,0.11];0.0;0.0;[4.145095678246545,4.606758320361752]","ode_id":"50b60b059fe3c06580c1632802cfc1f9","parameter_values":""},{"exact_solution":"","id":90,"initial_values":"0.7;0.0;0.0;1.362770287738494","ode_id":"50b60b059fe3c06580c1632802cfc1f9","parameter_values":""},{"exact_solution":"","id":91,"initial_values":"0.3;0.0;0.0;2.3804761428476167","ode_id":"50b60b059fe3c06580c1632802cfc1f9","parameter_values":""},{"exact_solution":"","id":92,"initial_values":"0.1;0.0;0.0;4.358898943540674","ode_id":"50b60b059fe3c06580c1632802cfc1f9","parameter_values":""}],"keywords":"","linearity":"NL","name":"Class D DETEST","parameter_count":0,"real_problem":false,"right_side":"x2;x3;-x0/sqrt((x0**2+x1**2)**3));-x1/sqrt((x0**2+x1**2)**3)","variable_count":4},{"accepted":true,"classification":"PI","complexity":"A","description":"","exact_solution":"exp(-t)*(((c1+c0)/sqrt(2.0))*sin(sqrt(2.0)*t)+c0*cos(sqrt(2.0)*t));exp(-t)*(-1.0*((c1+3.0*c0)/sqrt(2.0))*sin(sqrt(2.0)*t)+c1*cos(sqrt(2.0)*t))","id":"26e8b8e15b869cfcc410f04e8ac3e283","ivps":[{"exact_solution":"exp(-t)*(((-1.0+0.0)/sqrt(2.0))*sin(sqrt(2.0)*t)+0.0*cos(sqrt(2.0)*t));exp(-t)*(-1.0*((-1.0+3.0*0.0)/sqrt(2.0))*sin(sqrt(2.0)*t)+(-1.0)*cos(sqrt(2.0)*t))","id":45,"initial_values":"0.0;-1.0","ode_id":"26e8b8e15b869cfcc410f04e8ac3e283","parameter_values":""},{"exact_solution":"exp(-t)*((([-1.05,-0.9]+[0.0,0.1])/sqrt(2.0))*sin(sqrt(2.0)*t)+[0.0,0.1]*cos(sqrt(2.0)*t));exp(-t)*(-1.0*(([-1.05,-0.9]+3.0*[0.0,0.1])/sqrt(2.0))*sin(sqrt(2.0)*t)+[-1.05,-0.9]*cos(sqrt(2.0)*t))","id":115,"initial_values":"[0.0,0.1];[-1.05,-0.9]","ode_id":"26e8b8e15b869cfcc410f04e8ac3e283","parameter_values":""}],"keywords":"","linearity":"L","name":"Damped vibrations","parameter_count":0,"real_problem":false,"right_side":"x1;-2.0*x1-3.0*x0","variable_count":2},{"accepted":true,"classification":"PI","complexity":"B","description":"Equations of motion for the double pendulum model derived automatically with the program Maple.","exact_solution":"","id":"3ca6ccb2a35117347611d11b3e55f310","ivps":[{"exact_solution":"","id":126,"initial_values":"2.355;-1.727;0.43;0.67","ode_id":"3ca6ccb2a35117347611d11b3e55f310","parameter_values":"1.0;1.0"},{"exact_solution":"","id":127,"initial_values":"[1.855,2.855];-1.727;0.43;0.67","ode_id":"3ca6ccb2a35117347611d11b3e55f310","parameter_values":"1.0;1.0"},{"exact_solution":"","id":128,"initial_values":"2.355;-1.727;0.43;0.67","ode_id":"3ca6ccb2a35117347611d11b3e55f310","parameter_values":"[0.5,1.5];1.0"},{"exact_solution":"","id":129,"initial_values":"[2.255,2.455];-1.727;0.43;0.67","ode_id":"3ca6ccb2a35117347611d11b3e55f310","parameter_values":"[0.9,1.1];1.0"}],"keywords":"chaotic","linearity":"NL","name":"Double Pendulum","parameter_count":2,"real_problem":false,"right_side":"x2;x3;-0.01*(200.0*par1*sin(x1)*x3*x2+100.0*par1*sin(x1)*(x3)**2-981.0*par1*sin(x0)-981.0*par0*sin(x0)+100.0*par1*cos(x1)*sin(x1)*(x2)**2+981.0*par1*sin(x0)*(cos(x1))**2+981.0*par1*cos(x1)*cos(x0)*sin(x1)+100.0*par1*sin(x1)*(x2)**2)/(-1.0*par1-1.0*par0+par1*(cos(x1))**2);0.01*(200.0*cos(x1)*par1*sin(x1)*x3*x2+100.0*cos(x1)*par1*sin(x1)*(x3)**2+981.0*par1*sin(x0)*(cos(x1))**2+981.0*par1*cos(x1)*cos(x0)*sin(x1)+200.0*par1*sin(x1)*x3*x2+100.0*par1*sin(x1)*(x3)**2-981.0*par1*sin(x0)-981.0*par0*sin(x0)+981.0*par1*cos(x0)*sin(x1)+200.0*par1*sin(x1)*(x2)**2+200.0*par1*cos(x1)*sin(x1)*(x2)**2+100.0*par0*sin(x1)*(x2)**2+981.0*par0*cos(x0)*sin(x1))/(-1.0*par1-1.0*par0+par1*(cos(x1))**2)","variable_count":4},{"accepted":true,"classification":"PI","complexity":"B","description":"Derived from Bessel's equation of order 1/2 with shifted origin (a linear second-order equation with variable coefficients).","exact_solution":"t;(c1*cos(t)+(c2+c1/2.0)*sin(t))/sqrt(t+1.0);(cos(t)*(c2+(c1-c1/(t+1))/2.0)-sin(t)*(c1+(c2+c1/2.0)/2.0/(t+1)))/sqrt(t+1.0)","id":"365ecb0af746b3c01fa9c927f6b63795","ivps":[{"exact_solution":"t;(0.6713967071418030*cos(t)+(0.0954005144747446+0.6713967071418030/2.0)*sin(t))/sqrt(t+1.0);(cos(t)*(0.0954005144747446+(0.6713967071418030-0.6713967071418030/(t+1))/2.0)-sin(t)*(0.6713967071418030+(0.0954005144747446+0.6713967071418030/2.0)/2.0/(t+1)))/sqrt(t+1.0)","id":64,"initial_values":"0.0;0.6713967071418030;0.0954005144747446","ode_id":"365ecb0af746b3c01fa9c927f6b63795","parameter_values":""},{"exact_solution":"t;([0.67,0.68]*cos(t)+(0.0954005144747446+[0.67,0.68]/2.0)*sin(t))/sqrt(t+1.0);(cos(t)*(0.0954005144747446+([0.67,0.68]-[0.67,0.68]/(t+1))/2.0)-sin(t)*([0.67,0.68]+(0.0954005144747446+[0.67,0.68]/2.0)/2.0/(t+1)))/sqrt(t+1.0)","id":65,"initial_values":"0.0;[0.67,0.68];0.0954005144747446","ode_id":"365ecb0af746b3c01fa9c927f6b63795","parameter_values":""}],"keywords":"variable coefficients","linearity":"L","name":"E1 DETEST","parameter_count":0,"real_problem":false,"right_side":"1.0;x2;-1.0*(x2/(x0+1.0))-(1.0-(1.0/(4.0*(x0+1.0)**2)))*x1","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"Van der Pol oscillator. A non-conservative oscillator with non-linear damping; stiff for large par0.","exact_solution":"","id":"2e36a4d242a362f949dd292f0d7d6181","ivps":[{"exact_solution":"","id":76,"initial_values":"2.0;0.0","ode_id":"2e36a4d242a362f949dd292f0d7d6181","parameter_values":"1.0"},{"exact_solution":"","id":109,"initial_values":"2.0;0.0","ode_id":"2e36a4d242a362f949dd292f0d7d6181","parameter_values":"2.0"},{"exact_solution":"","id":110,"initial_values":"[1.37,1.43];2.25","ode_id":"2e36a4d242a362f949dd292f0d7d6181","parameter_values":"1.0"},{"exact_solution":"","id":111,"initial_values":"[1.1,1.7];2.25","ode_id":"2e36a4d242a362f949dd292f0d7d6181","parameter_values":"1.0"},{"exact_solution":"","id":112,"initial_values":"[0.8,2.0];2.25","ode_id":"2e36a4d242a362f949dd292f0d7d6181","parameter_values":"1.0"},{"exact_solution":"","id":113,"initial_values":"[-0.1,2.9];2.25","ode_id":"2e36a4d242a362f949dd292f0d7d6181","parameter_values":"1.0"}],"keywords":"chaotic","linearity":"NL","name":"E2 DETEST","parameter_count":1,"real_problem":false,"right_side":"x1;par0*(1.0-x0**2)*x1-x0","variable_count":2},{"accepted":true,"classification":"PI","complexity":"B","description":"Derived from Duffing's equation.","exact_solution":"","id":"d3f410048b4f5aef406f66f942837bd8","ivps":[{"exact_solution":"","id":46,"initial_values":"0.0;0.0;0.0","ode_id":"d3f410048b4f5aef406f66f942837bd8","parameter_values":"2.78535"},{"exact_solution":"","id":47,"initial_values":"0.0;0.0;0.0","ode_id":"d3f410048b4f5aef406f66f942837bd8","parameter_values":"[2.78,2.79]"}],"keywords":"","linearity":"NL","name":"E3 DETEST","parameter_count":1,"real_problem":false,"right_side":"1.0;x2;(x1**3)/6.0-x1+2.0*sin(par0*x0)","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"Derived from the equation of motion for a falling body.","exact_solution":"2.5*log(cosh(sqrt(0.032*0.4)*t+log((sqrt(0.032)+sqrt(0.4)*c1)/(sqrt(0.032)-sqrt(0.4)*c1))))+c0-2.5*log((0.032+0.4*(c1**2))/(0.032-0.4*(c1**2)));sqrt(0.032/0.4)*(1.0-2.0/(exp(2.0*sqrt(0.032*0.4)*t+log((sqrt(0.032)+sqrt(0.4)*c1)/(sqrt(0.032)-sqrt(0.4)*c1)))+1))","id":"9d2c39c398c05cf2732767150163a2a2","ivps":[{"exact_solution":"2.5*log(cosh(sqrt(0.032*0.4)*t+log((sqrt(0.032)+sqrt(0.4)*0.0)/(sqrt(0.032)-sqrt(0.4)*0.0))))+30.0-2.5*log((0.032+0.4*(0.0**2))/(0.032-0.4*(0.0**2)));sqrt(0.032/0.4)*(1.0-2.0/(exp(2.0*sqrt(0.032*0.4)*t+log((sqrt(0.032)+sqrt(0.4)*0.0)/(sqrt(0.032)-sqrt(0.4)*0.0)))+1))","id":66,"initial_values":"30.0;0.0","ode_id":"9d2c39c398c05cf2732767150163a2a2","parameter_values":""},{"exact_solution":"2.5*log(cosh(sqrt(0.032*0.4)*t+log((sqrt(0.032)+sqrt(0.4)*0.0)/(sqrt(0.032)-sqrt(0.4)*0.0))))+[29.5,30.5]-2.5*log((0.032+0.4*(0.0**2))/(0.032-0.4*(0.0**2)));sqrt(0.032/0.4)*(1.0-2.0/(exp(2.0*sqrt(0.032*0.4)*t+log((sqrt(0.032)+sqrt(0.4)*0.0)/(sqrt(0.032)-sqrt(0.4)*0.0)))+1))","id":67,"initial_values":"[29.5,30.5];0.0","ode_id":"9d2c39c398c05cf2732767150163a2a2","parameter_values":""}],"keywords":"","linearity":"NL","name":"E4 DETEST","parameter_count":0,"real_problem":false,"right_side":"x1;0.032-0.4*x1**2","variable_count":2},{"accepted":true,"classification":"PI","complexity":"B","description":"Derived from a pursuit equation when the path of the pursued is a straight line","exact_solution":"t;-0.5*25.0*(c2+sqrt(c2**2+1.0))*log(25.0-t)-(1.0/(2.0*(c2+sqrt(c2**2+1.0))))*t+(1.0/(100.0*(c2+sqrt(c2**2+1.0)))*(t**2)+c1+25.0*(c2+sqrt(c2**2+1.0))*log(5.0);0.5*((25.0*(c2+sqrt(c2**2+1.0)))/(25.0-t)-1/(25.0*(c2+sqrt(c2**2+1.0)))*(25-t))","id":"063ab58a63138d628d9d60ec58c2e7c3","ivps":[{"exact_solution":"t;-0.5*25.0*(0.0+sqrt(0.0**2+1.0))*log(25.0-t)-(1.0/(2.0*(0.0+sqrt(0.0**2+1.0))))*t+(1.0/(100.0*(0.0+sqrt(0.0**2+1.0)))*(t**2)+0.0+25.0*(0.0+sqrt(0.0**2+1.0))*log(5.0);0.5*((25.0*(0.0+sqrt(0.0**2+1.0)))/(25.0-t)-1/(25.0*(0.0+sqrt(0.0**2+1.0)))*(25-t))","id":68,"initial_values":"0.0;0.0;0.0","ode_id":"063ab58a63138d628d9d60ec58c2e7c3","parameter_values":""},{"exact_solution":"t;-0.5*25.0*([0,0.25]+sqrt([0,0.25]**2+1.0))*log(25.0-t)-(1.0/(2.0*([0,0.25]+sqrt([0,0.25]**2+1.0))))*t+(1.0/(100.0*([0,0.25]+sqrt([0,0.25]**2+1.0)))*(t**2)+0.0+25.0*([0,0.25]+sqrt([0,0.25]**2+1.0))*log(5.0);0.5*((25.0*([0,0.25]+sqrt([0,0.25]**2+1.0)))/(25.0-t)-1/(25.0*([0,0.25]+sqrt([0,0.25]**2+1.0)))*(25-t))","id":69,"initial_values":"0.0;0.0;[0,0.25]","ode_id":"063ab58a63138d628d9d60ec58c2e7c3","parameter_values":""}],"keywords":"non-linear","linearity":"NL","name":"E5 DETEST","parameter_count":0,"real_problem":false,"right_side":"1.0;x2;sqrt(1.0+x2**2)*(1.0/(25.0-x0))","variable_count":3},{"accepted":true,"classification":"PI","complexity":"A","description":"","exact_solution":"c1*sin(2.0*t)/2.0+c0*cos(2.0*t);c1*cos(2.0*t)-2.0*c0*sin(2.0*t)","id":"51916fca24fbc4b52b9abaa3208f512c","ivps":[{"exact_solution":"1.0*sin(2.0*t)/2.0+1.0*cos(2.0*t);1.0*cos(2.0*t)-2.0*1.0*sin(2.0*t)","id":16,"initial_values":"1.0;1.0","ode_id":"51916fca24fbc4b52b9abaa3208f512c","parameter_values":""},{"exact_solution":"1.0*sin(2.0*t)/2.0+[0.5,1.0]*cos(2.0*t);1.0*cos(2.0*t)-2.0*[0.5,1.0]*sin(2.0*t)","id":17,"initial_values":"[0.5,1.0];1.0","ode_id":"51916fca24fbc4b52b9abaa3208f512c","parameter_values":""}],"keywords":"","linearity":"L","name":"Harmonic Oscillator 1","parameter_count":0,"real_problem":false,"right_side":"x1;-4.0*x0","variable_count":2},{"accepted":true,"classification":"PI","complexity":"A","description":"Derived from a second order linear equation with circular solution trajectories.","exact_solution":"-c1*sin(t)+c0*cos(t);c1*cos(t)+c0*sin(t)","id":"37bb61e77465620888c097647c5719ea","ivps":[{"exact_solution":"-[-1.0,0.0]*sin(t)+[0.0,1.0]*cos(t);[-1.0,0.0]*cos(t)+[0.0,1.0]*sin(t)","id":50,"initial_values":"[0.0,1.0];[-1.0,0.0]","ode_id":"37bb61e77465620888c097647c5719ea","parameter_values":""},{"exact_solution":"-(-1.0)*sin(t)+1.0*cos(t);-1.0*cos(t)+1.0*sin(t)","id":51,"initial_values":"1.0;-1.0","ode_id":"37bb61e77465620888c097647c5719ea","parameter_values":""},{"exact_solution":"-[0.95,1.05]*sin(t)+[0.0,0.1]*cos(t);[0.95,1.05]*cos(t)+[0.0,0.1]*sin(t)","id":74,"initial_values":"[0.0,0.1];[0.95,1.05]","ode_id":"37bb61e77465620888c097647c5719ea","parameter_values":""}],"keywords":"periodic;min test set","linearity":"L","name":"Harmonic Oscillator 2","parameter_count":0,"real_problem":false,"right_side":"-x1;x0","variable_count":2},{"accepted":true,"classification":"PI","complexity":"B","description":"Derived from linear equations with variable coefficients.","exact_solution":"","id":"9f782896c104a3d1dd956cddb21e5cde","ivps":[{"exact_solution":"","id":120,"initial_values":"2.0;3.0;0.0","ode_id":"9f782896c104a3d1dd956cddb21e5cde","parameter_values":""}],"keywords":"","linearity":"L","name":"Lambert 1","parameter_count":0,"real_problem":false,"right_side":"-2.0*x0+x1+2.0*sin(x2);998.0*x0-999.0*x1*999.0*(cos(x2)-sin(x2));1.0","variable_count":3},{"accepted":true,"classification":"PII","complexity":"B","description":"Integration must start at t=1 (test  intervals: [1,2] for C4/C5; [1,11] for C6).","exact_solution":"","id":"1b5613f8a7fb53e23af656bea8b3e289","ivps":[{"exact_solution":"","id":117,"initial_values":"1.0;0.3678794412;1.0","ode_id":"1b5613f8a7fb53e23af656bea8b3e289","parameter_values":""},{"exact_solution":"","id":125,"initial_values":"[0.9,1.1];[0.2678794412,0.4678794412];1.0","ode_id":"1b5613f8a7fb53e23af656bea8b3e289","parameter_values":""}],"keywords":"stiff","linearity":"NL","name":"Lambert 2","parameter_count":0,"real_problem":false,"right_side":"1.0/x0-x1*exp(x2**2)/(x2**2)-x2;1.0/x1-exp(x2**2)-2.0*x2*exp(-x2*x2);1.0","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"A chaotic system of ordinary differential equations. Applications such as simplified models for lasers, electric circuits, chemical reactions or atmospheric convection.","exact_solution":"","id":"b4c6cc6c5b39dd72a54f527a8bb29842","ivps":[{"exact_solution":"","id":78,"initial_values":"15.0;15.0;36.0","ode_id":"b4c6cc6c5b39dd72a54f527a8bb29842","parameter_values":"10.0;2.66666;15.0"},{"exact_solution":"","id":93,"initial_values":"15.0;15.0;36.0","ode_id":"b4c6cc6c5b39dd72a54f527a8bb29842","parameter_values":"10.0;2.66666;28.0"}],"keywords":"non-periodic;chaotic","linearity":"NL","name":"Lorenz 1 (Classic Form)","parameter_count":3,"real_problem":false,"right_side":"par0*(x1-x0);x0*(par2-x2)-x1;x0*x1-par1*x2","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"See Lorenz 1 (Classic Form); here the Jordan normal form exhibits more chaotic behavior for smaller values of the first initial condition.","exact_solution":"","id":"a0b502ae83d4cd6b89da82af3c6129ab","ivps":[{"exact_solution":"","id":98,"initial_values":"0.92;2.21;27.0","ode_id":"a0b502ae83d4cd6b89da82af3c6129ab","parameter_values":""},{"exact_solution":"","id":99,"initial_values":"0.88;2.21;27.0","ode_id":"a0b502ae83d4cd6b89da82af3c6129ab","parameter_values":""},{"exact_solution":"","id":100,"initial_values":"0.84;2.21;27.0","ode_id":"a0b502ae83d4cd6b89da82af3c6129ab","parameter_values":""},{"exact_solution":"","id":101,"initial_values":"[0.915,0.925];[2.205,2.215];27.0","ode_id":"a0b502ae83d4cd6b89da82af3c6129ab","parameter_values":""},{"exact_solution":"","id":102,"initial_values":"[0.875,0.885];[2.205,2.215];27.0","ode_id":"a0b502ae83d4cd6b89da82af3c6129ab","parameter_values":""},{"exact_solution":"","id":103,"initial_values":"[0.835,0.845];[2.205,2.215];27.0","ode_id":"a0b502ae83d4cd6b89da82af3c6129ab","parameter_values":""}],"keywords":"non-periodic;chaotic;min test set","linearity":"NL","name":"Lorenz 2 (Jordan NF)","parameter_count":0,"real_problem":false,"right_side":"11.8*x0-0.29*(x0+x1)*x2;-22.8*x1+0.29*(x0+x1)*x2;-2.67*x2+(x0+x1)*(2.2*x0-1.3*x1)","variable_count":3},{"accepted":true,"classification":"PII","complexity":"B","description":"Predator-prey equations; a system of two first-order non-linear differential equations.","exact_solution":"","id":"81c92c54b7645184f96b4c1b9733591b","ivps":[{"exact_solution":"","id":75,"initial_values":"1.0;3.0","ode_id":"81c92c54b7645184f96b4c1b9733591b","parameter_values":""},{"exact_solution":"","id":114,"initial_values":"[0.95,1.05];[2.95,3.05]","ode_id":"81c92c54b7645184f96b4c1b9733591b","parameter_values":""}],"keywords":"periodic;stiff","linearity":"NL","name":"Lotka-Volterra","parameter_count":0,"real_problem":false,"right_side":"2.0*x0*(1.0-x1);-x1*(1.0-x0)","variable_count":2},{"accepted":true,"classification":"PI","complexity":"B","description":"","exact_solution":"","id":"11fdae44347956f76a50a9538cbf143a","ivps":[{"exact_solution":"","id":30,"initial_values":"[0.5,1.5];[0.8,1.2];[0.4,1.6]","ode_id":"11fdae44347956f76a50a9538cbf143a","parameter_values":""},{"exact_solution":"","id":31,"initial_values":"1.0;1.0;1.0","ode_id":"11fdae44347956f76a50a9538cbf143a","parameter_values":""}],"keywords":"non-linear","linearity":"NL","name":"Nonlinear Degree 3","parameter_count":0,"real_problem":false,"right_side":"-2.0*x1+x1*x2-x0**3;x0-x0*x2-x1**3;x0*x1-x2**3","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"","exact_solution":"","id":"3ed29345ac3b037eca8ee38ab1cc0aac","ivps":[{"exact_solution":"","id":28,"initial_values":"[0.2,1.0];[0.5,1.0]","ode_id":"3ed29345ac3b037eca8ee38ab1cc0aac","parameter_values":""},{"exact_solution":"","id":29,"initial_values":"1.0;1.0","ode_id":"3ed29345ac3b037eca8ee38ab1cc0aac","parameter_values":""}],"keywords":"non-linear","linearity":"NL","name":"Nonlinear Degree 4","parameter_count":0,"real_problem":false,"right_side":"x0**2*x1**2-x0**4-x0*x1**2+x0**3-x1**4;-1.0*x1**3+x0**2*x1","variable_count":2},{"accepted":true,"classification":"PII","complexity":"A","description":"A stiff problem with par0 as the stiffness coefficient (the smaller, the stiffer).","exact_solution":"","id":"2e4b81c41405991e0a7df835bb99f245","ivps":[{"exact_solution":"","id":73,"initial_values":"10.0;0.0","ode_id":"2e4b81c41405991e0a7df835bb99f245","parameter_values":"0.001"},{"exact_solution":"","id":104,"initial_values":"10.0;0.0","ode_id":"2e4b81c41405991e0a7df835bb99f245","parameter_values":"0.01"},{"exact_solution":"","id":105,"initial_values":"10.0;0.0","ode_id":"2e4b81c41405991e0a7df835bb99f245","parameter_values":"0.1"}],"keywords":"non-periodic;stiff;min test set","linearity":"NL","name":"Oil reservoir problem","parameter_count":1,"real_problem":false,"right_side":"x1;x1**2-(3.0/(par0+x0**2))","variable_count":2},{"accepted":true,"classification":"PI","complexity":"B","description":"Shifted orbit equations.","exact_solution":"","id":"370ce4f580b4903af42480d2167c358f","ivps":[{"exact_solution":"","id":124,"initial_values":"0.994;0.0;0.0;-2.00158510637908252240537862224","ode_id":"370ce4f580b4903af42480d2167c358f","parameter_values":"0.012277471;0.987722529"}],"keywords":"","linearity":"NL","name":"Orbit Equations","parameter_count":2,"real_problem":false,"right_side":"x2;x3;x0+2.0*x3-par1*(x0+par0)/(sqrt((x0+par0)**2+x1**2)*((x0+par0)**2+x1**2))-par0*(x0-par1)/(sqrt((x0-par1)**2+x1**2)*((x0-par1)**2+x1**2));x1-2.0*x2-par1*x1/(sqrt((x0+par0)**2+x1**2)*((x0+par0)**2+x1**2))-par0*x1/(sqrt((x0-par1)**2+x1**2)*((x0-par1)**2+x1**2))","variable_count":4},{"accepted":true,"classification":"PI","complexity":"A","description":"A simple second order linear equation with constant coefficients.","exact_solution":"(3.0*c0+c1)/6.0*exp(3.0*t)+(3.0*c0-c1)/6.0*exp(-3.0*t);(3.0*c0+c1)/2.0*exp(3.0*t)-(3.0*c0-c1)/2.0*exp(-3.0*t)","id":"535819d6202287cdbadb00e672231072","ivps":[{"exact_solution":"(3.0*1.0+1.0)/6.0*exp(3.0*t)+(3.0*1.0-1.0)/6.0*exp(-3.0*t);(3.0*1.0+1.0)/2.0*exp(3.0*t)-(3.0*1.0-1.0)/2.0*exp(-3.0*t)","id":18,"initial_values":"1.0;1.0","ode_id":"535819d6202287cdbadb00e672231072","parameter_values":""},{"exact_solution":"(3.0*1.0+[0.5,1.0])/6.0*exp(3.0*t)+(3.0*1.0-[0.5,1.0])/6.0*exp(-3.0*t);(3.0*1.0+[0.5,1.0])/2.0*exp(3.0*t)-(3.0*1.0-[0.5,1.0])/2.0*exp(-3.0*t)","id":19,"initial_values":"1.0;[0.5,1.0]","ode_id":"535819d6202287cdbadb00e672231072","parameter_values":""}],"keywords":"simple;linear;constant coefficients","linearity":"L","name":"Simple Linear 1","parameter_count":0,"real_problem":false,"right_side":"x1;9.0*x0","variable_count":2},{"accepted":true,"classification":"PI","complexity":"A","description":"A simple second order equation with constant coefficients.","exact_solution":"(c0+c1)*exp(t)/2.0+(c0-c1)/2.0*exp(-t);(c0+c1)*exp(t)/2.0-(c0-c1)/2.0*exp(-t)\r\n","id":"3611cac04a39579411d5695fe2bd2d5f","ivps":[{"exact_solution":"([-1,0.1]+[0.9,1.1])*exp(t)/2.0+([-1,0.1]-[0.9,1.1])/2.0*exp(-t);([-1,0.1]+[0.9,1.1])*exp(t)/2.0-([-1,0.1]-[0.9,1.1])/2.0*exp(-t)\r\n","id":24,"initial_values":"[-1,0.1];[0.9,1.1]","ode_id":"3611cac04a39579411d5695fe2bd2d5f","parameter_values":""},{"exact_solution":"(-1.0+1.0)*exp(t)/2.0+(-1.0-1.0)/2.0*exp(-t);(-1.0+1.0)*exp(t)/2.0-(-1.0-1.0)/2.0*exp(-t)\r\n","id":25,"initial_values":"-1.0;1.0","ode_id":"3611cac04a39579411d5695fe2bd2d5f","parameter_values":""}],"keywords":"simple;linear;constant coefficients","linearity":"L","name":"Simple Linear 2","parameter_count":0,"real_problem":false,"right_side":"x1;x0","variable_count":2},{"accepted":true,"classification":"PI","complexity":"A","description":"A non-linear separable ODE.","exact_solution":"1.0/(1.0/c0-t)","id":"999b36729ed4601f3642277321daebee","ivps":[{"exact_solution":"1.0/(1.0/5.0-t)","id":8,"initial_values":"5.0","ode_id":"999b36729ed4601f3642277321daebee","parameter_values":""},{"exact_solution":"1.0/(1.0/[-1.5,-0.5]-t)","id":85,"initial_values":"[-1.5,-0.5]","ode_id":"999b36729ed4601f3642277321daebee","parameter_values":""}],"keywords":"","linearity":"NL","name":"Simple Nonlinear 1","parameter_count":0,"real_problem":false,"right_side":"x0**2","variable_count":1},{"accepted":true,"classification":"PI","complexity":"A","description":"A non-linear separable ODE.","exact_solution":"1.0-(2.0/((2.0/(1.0-c0)-1.0)*exp(2.0*t)+1.0))","id":"9fb6152e595a7eff1e82d90ab0ab819a","ivps":[{"exact_solution":"1.0-(2.0/((2.0/(1.0-[3.9,4.1])-1.0)*exp(2.0*t)+1.0))","id":22,"initial_values":"[3.9,4.1]","ode_id":"9fb6152e595a7eff1e82d90ab0ab819a","parameter_values":""},{"exact_solution":"1.0-(2.0/((2.0/(1.0-4.0)-1.0)*exp(2.0*t)+1.0))","id":23,"initial_values":"4.0","ode_id":"9fb6152e595a7eff1e82d90ab0ab819a","parameter_values":""}],"keywords":"","linearity":"NL","name":"Simple Nonlinear 2","parameter_count":0,"real_problem":false,"right_side":"1.0-x0**2","variable_count":1},{"accepted":true,"classification":"PI","complexity":"A","description":"A non-linear separable ODE.","exact_solution":"sin(t+asin(c0))","id":"3b2e70e580480932aa9496fcd5e63b0e","ivps":[{"exact_solution":"sin(t+asin(0.2))","id":43,"initial_values":"0.2","ode_id":"3b2e70e580480932aa9496fcd5e63b0e","parameter_values":""},{"exact_solution":"sin(t+asin([0.1,0.3]))","id":44,"initial_values":"[0.1,0.3]","ode_id":"3b2e70e580480932aa9496fcd5e63b0e","parameter_values":""}],"keywords":"","linearity":"NL","name":"Simple Nonlinear 3","parameter_count":0,"real_problem":false,"right_side":"sqrt(1.0-x0**2)","variable_count":1},{"accepted":true,"classification":"PII","complexity":"A","description":"A simple linear system of equations which is stiff for certain initial conditions.","exact_solution":"3.0*(c1-c0)/5.0*exp(-t)-(3.0*c1-2.0*c0)/5.0*exp(-200.0*t);2.0*(c1-c0)/5.0*exp(-t)+(3.0*c1-2.0*c0)/5.0*exp(-200.0*t)","id":"a8494b15a9387ffcb3d477db7dedccd2","ivps":[{"exact_solution":"3.0*(5.0-0.0)/5.0*exp(-t)-(3.0*5.0-2.0*0.0)/5.0*exp(-200.0*t);2.0*(5.0-0.0)/5.0*exp(-t)+(3.0*5.0-2.0*0.0)/5.0*exp(-200.0*t)","id":130,"initial_values":"0.0;5.0","ode_id":"a8494b15a9387ffcb3d477db7dedccd2","parameter_values":""},{"exact_solution":"3.0*([4.55,5.05]-[0.0,1.0])/5.0*exp(-t)-(3.0*[4.55,5.05]-2.0*[0.0,1.0])/5.0*exp(-200.0*t);2.0*([4.55,5.05]-[0.0,1.0])/5.0*exp(-t)+(3.0*[4.55,5.05]-2.0*[0.0,1.0])/5.0*exp(-200.0*t)","id":131,"initial_values":"[0.0,1.0];[4.55,5.05]","ode_id":"a8494b15a9387ffcb3d477db7dedccd2","parameter_values":""}],"keywords":"stiff","linearity":"L","name":"Simple Stiff 1","parameter_count":0,"real_problem":false,"right_side":"-80.6*x0+119.4*x1;79.6*x0-120.4*x1","variable_count":2},{"accepted":true,"classification":"PI","complexity":"C","description":"A simplified biological wastewater treatment process model.","exact_solution":"","id":"51fcc00bb1a3ebead92a9bba0bc0b901","ivps":[{"exact_solution":"","id":14,"initial_values":"0.616;0.1;0.00265;0.001","ode_id":"51fcc00bb1a3ebead92a9bba0bc0b901","parameter_values":"67.0;2.0;2.0;694.0;72.0;8000.0;15278.0;616.0;9167.0;5.0;53.0;4545.0;5.0;4872.0;1428.0"},{"exact_solution":"","id":108,"initial_values":"[0.61,0.62];0.1;0.00265;0.001","ode_id":"51fcc00bb1a3ebead92a9bba0bc0b901","parameter_values":"67.0;2.0;2.0;694.0;72.0;8000.0;15278.0;616.0;9167.0;5.0;53.0;4545.0;5.0;4872.0;1428.0"}],"keywords":"","linearity":"NL","name":"Simplified ASM1","parameter_count":14,"real_problem":false,"right_side":"par6/par5*(par7-x0)-par3/(1.0+par1/x0)/(1.0+par2/x2)/par0*x1;par6/par5*x1+par8/par5*(x3-x1)+(par3/(1.0+par1/x0)/(1.0+par2/x2)-par4)*x1;par6/par5*(par9-x2)-par3/(1.0+par1/x0)/(1.0+par2/x2)*(1.0-par0)/par0*x1+(1.0-x2/par10)*par13*par14/par5;1.0/par11*((par6+par8)*x1-(par12+par8)*x3)","variable_count":4},{"accepted":true,"classification":"PI","complexity":"B","description":"A chaotic system of equations useful for modeling equilibrium in chemical reactions.","exact_solution":"","id":"acade8b3eb9f15b52dc69da4192e6071","ivps":[{"exact_solution":"","id":77,"initial_values":"0.0;-10.3;0.03","ode_id":"acade8b3eb9f15b52dc69da4192e6071","parameter_values":"0.2;0.2;5.7"},{"exact_solution":"","id":106,"initial_values":"[-0.0001,0.0001];[-10.3001,-10.2999];[0.0299,0.0301]","ode_id":"acade8b3eb9f15b52dc69da4192e6071","parameter_values":"0.2;0.2;5.7"},{"exact_solution":"","id":107,"initial_values":"[-0.2,0.2];[-9.58095,-9.18095];[-0.1704098,0.2295902]","ode_id":"acade8b3eb9f15b52dc69da4192e6071","parameter_values":"0.2;0.2;5.7"}],"keywords":"chaotic","linearity":"NL","name":"The Roessler Attractor","parameter_count":3,"real_problem":false,"right_side":"-1.0*(x1+x2);x0+par0*x1;par1+x2*(x0-par2)","variable_count":3},{"accepted":true,"classification":"PI","complexity":"B","description":"A standard example in parameter optimization; describes the way materials or energies are transmitted among the compartments. Please note that the supplied exact solution is correct only for certain \r\ninitial conditions (e.g., those from the IVPs).","exact_solution":"((par1-0.5*(par0+par1+par2-sqrt((par0-par1+par2)**2+4*par1*par2)))*exp(-0.5*(par0+par1+par2-sqrt((par0-par1+par2)**2+4*par1*par2))*t)-(par1-0.5*(par0+par1+par2+sqrt((par0-par1+par2)**2+4*par1*par2)))*exp(-0.5*(par0+par1+par2+sqrt((par0-par1+par2)**2+4*par1*par2))*t))/sqrt((par0-par1+par2)**2+4*par1*par2);par2*(exp(-0.5*(par0+par1+par2-sqrt((par0-par1+par2)**2+4*par1*par2))*t)-exp(-0.5*(par0+par1+par2+sqrt((par0-par1+par2)**2+4*par1*par2))*t))/sqrt((par0-par1+par2)**2+4*par1*par2)","id":"c1e84cdd908f57754ca599e962cfa75c","ivps":[{"exact_solution":"((0.232718-0.5*(1.925403+0.232718+0.145076-sqrt((1.925403-0.232718+0.145076)**2+4*0.232718*0.145076)))*exp(-0.5*(1.925403+0.232718+0.145076-sqrt((1.925403-0.232718+0.145076)**2+4*0.232718*0.145076))*t)-(0.232718-0.5*(1.925403+0.232718+0.145076+sqrt((1.925403-0.232718+0.145076)**2+4*0.232718*0.145076)))*exp(-0.5*(1.925403+0.232718+0.145076+sqrt((1.925403-0.232718+0.145076)**2+4*0.232718*0.145076))*t))/sqrt((1.925403-0.232718+0.145076)**2+4*0.232718*0.145076);0.145076*(exp(-0.5*(1.925403+0.232718+0.145076-sqrt((1.925403-0.232718+0.145076)**2+4*0.232718*0.145076))*t)-exp(-0.5*(1.925403+0.232718+0.145076+sqrt((1.925403-0.232718+0.145076)**2+4*0.232718*0.145076))*t))/sqrt((1.925403-0.232718+0.145076)**2+4*0.232718*0.145076)","id":118,"initial_values":"1.0;0.0","ode_id":"c1e84cdd908f57754ca599e962cfa75c","parameter_values":"1.925403;0.232718;0.145076"},{"exact_solution":"(([0.2,0.3]-0.5*([1.9,2.0]+[0.2,0.3]+[0.1,0.2]-sqrt(([1.9,2.0]-[0.2,0.3]+[0.1,0.2])**2+4*[0.2,0.3]*[0.1,0.2])))*exp(-0.5*([1.9,2.0]+[0.2,0.3]+[0.1,0.2]-sqrt(([1.9,2.0]-[0.2,0.3]+[0.1,0.2])**2+4*[0.2,0.3]*[0.1,0.2]))*t)-([0.2,0.3]-0.5*([1.9,2.0]+[0.2,0.3]+[0.1,0.2]+sqrt(([1.9,2.0]-[0.2,0.3]+[0.1,0.2])**2+4*[0.2,0.3]*[0.1,0.2])))*exp(-0.5*([1.9,2.0]+[0.2,0.3]+[0.1,0.2]+sqrt(([1.9,2.0]-[0.2,0.3]+[0.1,0.2])**2+4*[0.2,0.3]*[0.1,0.2]))*t))/sqrt(([1.9,2.0]-[0.2,0.3]+[0.1,0.2])**2+4*[0.2,0.3]*[0.1,0.2]);[0.1,0.2]*(exp(-0.5*([1.9,2.0]+[0.2,0.3]+[0.1,0.2]-sqrt(([1.9,2.0]-[0.2,0.3]+[0.1,0.2])**2+4*[0.2,0.3]*[0.1,0.2]))*t)-exp(-0.5*([1.9,2.0]+[0.2,0.3]+[0.1,0.2]+sqrt(([1.9,2.0]-[0.2,0.3]+[0.1,0.2])**2+4*[0.2,0.3]*[0.1,0.2]))*t))/sqrt(([1.9,2.0]-[0.2,0.3]+[0.1,0.2])**2+4*[0.2,0.3]*[0.1,0.2])","id":119,"initial_values":"1.0;0.0","ode_id":"c1e84cdd908f57754ca599e962cfa75c","parameter_values":"[1.9,2.0];[0.2,0.3];[0.1,0.2]"}],"keywords":"cooperative;min test set","linearity":"L","name":"Two Compartment Model","parameter_count":3,"real_problem":false,"right_side":"-(par2+par0)*x0+par1*x1;par2*x0-par1*x1","variable_count":2}]