Clearly $\displaystyle \ddot x -2 \dot x -3x=10 \sin t$ is not a linear equation.Write $\displaystyle \ddot x -2 \dot x -3x=10 \sin t$ in the three variables $\displaystyle x, \ y= \dot x$ and $\displaystyle \dot s =1$ so that the equations are autonomous and first order.

My lecture notes state that "nonlinear equations cannot be written in the form $\displaystyle \dot x = Ax$ (where $\displaystyle x \in \mathbb{R}^n$ and $\displaystyle A$ is an $\displaystyle n \times n$ matrix)".

So isn't this question literally asking me to do the impossible??