8.2.2.6 Systems of differential equations

Problem: Solve the system of differential equations using the operational method: \[ \left\{\begin{array}{l} \dot{x}=x+2 y+1-t-2 e^{3 t} \\ \dot{y}=2 x+3 y-2 t \end{array} x(0)=0, \quad y(0)=1 .\right. \]