Chapter 3.2, Problem 10P

$\left(a\right)$ Show that the functions

$x\left(t\right)=e^{-t}\left(2\cos 2t-\sin 2t\right)$

$y\left(t\right)=-e^{-t}\left(2\sin 2t+\cos 2t\right)$

Are solutions of the system

$x\text{'}=-x+2y$,

$y\text{'}=-2x-y$,

Satisfying the initial conditions $x\left(0\right)=2$ and $y\left(0\right)=-1$.

$\left(b\right)$ Use a computer to plot the graphs of $x$ and $y$ versus $t$.