Derive the linearized model for the nonlinear system, described by [begin{cases}dot{x}_{1}=x_{1}left|x_{1} ight|+x_{2}-1+sin t & x_{1}(0)=-1 dot{x}_{2}=-x_{1}-x_{2}-1

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Derive the linearized model for the nonlinear system, described by

\[\begin{cases}\dot{x}_{1}=x_{1}\left|x_{1}\right|+x_{2}-1+\sin t & x_{1}(0)=-1 \\ \dot{x}_{2}=-x_{1}-x_{2}-1 & x_{2}(0)=0\end{cases}\]

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