Chapter 3.2, Problem 11P

$\left(a\right)$ Show that

$x=\left(\begin{array}{l}\sin t-t\cos t\\ t\sin t\end{array}\right)$

issolution of the system

$x\text{'}=(\begin{array}{l}01\\ -10\end{array})x+(\begin{array}{l}0\\ 2\sin t\end{array})$,

Satisfying the initial condition

$x\left(0\right)=\left(\begin{array}{l}0\\ 0\end{array}\right)$.

$\left(b\right)$ Use a computer to draw component plots of $x$.