$$\begin{align}\dot{x}_{0}&=- 2.0 \cdot x_{0} + x_{1} + 2.0 \cdot \sin {x_{2}}\\\dot{x}_{1}&=998.0 \cdot x_{0} - 998001.0 \cdot x_{1} \cdot \left(- \sin {x_{2}} + \cos {x_{2}}\right)\\\dot{x}_{2}&=1.0\end{align}$$
Derived from linear equations with variable coefficients.
$$\begin{align}x_{0}(0)&=2.0\\x_{1}(0)&=3.0\\x_{2}(0)&=0.0\end{align}$$
No exact solution provided.
[untested]
* rounded (non-rigorously) to 5 decimal places to preserve screen real estate.