Chapter 5.6, Problem 9P

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.

$y\text{'}\text{'}+y\text{'}=g(t);$ $y(0)=6,$ $y\text{'}(0)=8;$

$g(t)=\{\begin{array}{c}t/2,\\ 3,\end{array}\begin{array}{c}0\le t<6\\ t\ge 6\end{array}$