Solve the following system:
\begin{aligned}&x^{\prime}=4 x-y+t^{2} \\&y^{\prime}=x+2 y+3 t\end{aligned}\quad\quad\quad\quad\quad (12)Solve the following system:
\begin{aligned}&x^{\prime}=4 x-y+t^{2} \\&y^{\prime}=x+2 y+3 t\end{aligned}\quad\quad\quad\quad\quad (12)