Chapter 9.11, Problem 27AP

For Problems $25-29$, use the variation-of-parameters method to determine a particular solution to the nonhomogeneous linear system $x\text{'}=Ax+b$. Also find the general solution to the system.

$A=\left[\begin{array}{cc}10& -4\\ 4& 2\end{array}\right]$, $b=\left[\begin{array}{c}0\\ \frac{1}{t}{e}^{6t}\end{array}\right]$.