Let \(\displaystyle{\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}}={v}\) (1), then we have

\(\displaystyle{\frac{{{d}}}{{{\left.{d}{t}\right.}}}}{\left({\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}}\right)}+{\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}}={x}\)

\(\displaystyle\Rightarrow{\frac{{{d}{v}}}{{{\left.{d}{t}\right.}}}}+{v}={x}\) (2)

From (1) and (2), we have the system

\(\displaystyle{\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}}={0}{x}+{v}\)

\(\displaystyle{\frac{{{d}{v}}}{{{\left.{d}{t}\right.}}}}={x}-{v}\)

\(\Rightarrow \begin{bmatrix}\frac{dx}{dt} \\ \frac{dv}{dt} \end{bmatrix}=\begin{bmatrix}0 & 1 \\ 1 & -1 \end{bmatrix} \begin{bmatrix} x \\ v \end{bmatrix}\)