Chapter 9.6, Problem 5P

Problems

For Problems $1-9$, use the variation of parameters technique to find a particular solution $x_p$ to $x^{\prime }=Ax+b$, for the given system $A$ and $b$. Also obtain the general solution to the system of differential equations.

$A=\left[\begin{array}{cc}-1& 2\\ -2& 4\end{array}\right]$, $b=\left[\begin{array}{c}54t{e}^{3t}\\ 9e^{3t}\end{array}\right]$