$$\begin{align}\dot{x}_{0}&=1.0\\\dot{x}_{1}&=x_{2}\\\dot{x}_{2}&=0.166666666666667 \cdot x_{1}^{3} - x_{1} + 2.0 \cdot \sin {par_{0} \cdot x_{0}}\end{align}$$
Derived from Duffing's equation. Link to DETEST description
$$\begin{align}x_{0}(0)&=0.0\\x_{1}(0)&=0.0\\x_{2}(0)&=0.0\end{align}$$
$$\begin{align}par_{0}&=2.78535\end{align}$$
No exact solution provided.
[untested]
$$\begin{align}par_{0}&\subset~\left[ 2.78, 2.79\right]\end{align}$$
* rounded (non-rigorously) to 5 decimal places to preserve screen real estate.