8.2.2.8 Systems of differential equations

condition: Integrate the system of linear differential equations under given initial conditions: \[ \left\{\begin{array}{l} x^{\prime \prime}-x^{\prime}+y^{\prime}=e^{-t}+\cos t \\ x^{\prime}-y^{\prime \prime}-y^{\prime}=2 e^{t}+\sin t^{\prime} \end{array}\right. \] \[ t=0, \quad x=2, \quad x^{\prime}=1, y=0, \quad y^{\prime}=1 \]