8.3.3 Systems of ordinary differential equations

Problem: Find the general solution of the inhomogeneous system of differential equations: \[ \left\{\begin{array}{c} x^{\prime}=6 x-2 y-z+5 \\ y^{\prime}=-x+5 y-z+e^{t} \\ z^{\prime}=x-2 y+4 z+2 \end{array}\right. \]