8.3.1 Systems of ordinary differential equations

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