Chapter 5.6, Problem 2P

In each of Problems $1$ through $13$, find the solutions of the given initial value problem. Draw the graphs of the solution and of the forcing function; explain how they are related.

$y\text{'}\text{'}+2y\text{'}+2y=h(t);$ $y(0)=5,$ $y\text{'}(0)=4;$

$h(t)=\{\begin{array}{c}1,\pi \le t<2\pi \\ 0,0\le t<\pi \text{and t}\ge \text{2}\pi \end{array}$