Chapter 5.4, Problem 21P

In each of Problems $20$ through $24$, use a computer algebra system to assist in solving the given initial value problem by the method of Laplace transforms:

$y\text{'}=\left(\begin{array}{cc}5& -1\\ 1& 3\end{array}\right)y+\left(\begin{array}{c}{e}^{-t}\\ 2e^t\end{array}\right),y\left(0\right)=\left(\begin{array}{c}-3\\ 2\end{array}\right)$.