8.2.2.3 Systems of differential equations

Problem: Solve the inhomogeneous system of differential equations, applying the operational method. \[ \left\{\begin{array}{cc} x_{1}^{\prime}=4 x_{1}-16 x_{2}+11 x_{3}-10 & x_{1}(0)=5 \\ x_{2}^{\prime}=-3 x_{1}+9 x_{2}-7 x_{3}+8, & x_{2}(0)=0 \\ x_{3}^{\prime}=-6 x_{1}+20 x_{2}-15 x_{3}+16 & x_{3}(0)=-1 \end{array}\right. \]