8.2.2.2 Systems of differential equations

Problem: Solve the inhomogeneous system of differential equations, using the operational method. \[ \left\{\begin{array}{ll} x_{1}^{\prime}=5 x_{1}-18 x_{2}-28 e^{-t} & x_{1}(0)=-1 \\ x_{2}^{\prime}=2 x_{1}-7 x_{2}-9 e^{-t} & x_{2}(0)=-2 \end{array}\right. \]