Lotka-Volterra

$$\begin{align}\dot{x}_{0}&=2.0 \cdot x_{0} \cdot \left(1.0 - x_{1}\right)\\\dot{x}_{1}&=- x_{1} \cdot \left(1.0 - x_{0}\right)\end{align}$$

Predator-prey equations; a system of two first-order non-linear differential equations.

periodic; stiff

$$\begin{align}x_{0}(0)&=1.0\\x_{1}(0)&=3.0\end{align}$$

No exact solution provided.

[untested]

$$\begin{align}x_{0}(0)&\subset~\left[ 0.95, 1.05\right]\\x_{1}(0)&\subset~\left[ 2.95, 3.05\right]\end{align}$$

No exact solution provided.

[untested]

^* rounded (non-rigorously) to 5 decimal places to preserve screen real estate.