8.3.2 Systems of ordinary differential equations

Problem: Find the general solution of the inhomogeneous system of differential equations: \[ \left\{\begin{array}{l} x_{t}^{\prime}=3 x-4 y+e^{-2 t} \\ y_{t}^{\prime}=x-2 y-3 e^{-2 t} \end{array}\right. \]