Chapter 9.7, Problem 9E

In Problems 7-10, use the method of undetermined coefficient to determine only the form of a particular solution for the system $x^{\prime }\left(t\right)=Ax\left(t\right)+f\left(t\right)$, where A and $f\left(t\right)$ are given.

$A=\left[\begin{array}{ccc}0& -1& 0\\ -1& 0& 1\\ 0& 0& 1\end{array}\right],f\left(t\right)=\left[\begin{array}{c}{e}^{2t}\\ \sin t\\ t\end{array}\right]$