Consider the following initial value problem:
y" + 12y' + 32y = f(t); y(0) = 0, y'(0) = 0;
f(t) = \begin{cases} 1, & 0 \le t < 10 \\ 0, & t \ge 10 \end{cases}
(a) Sketch the graph of the forcing function on an appropriate interval.
(b) Find the solution of the given initial value problem.
NOTE: Denote the Heaviside function by $u_c(t)$ where $u_c(t) = 1$ if $t \ge c$ and 0 otherwise.
Indicate separately the value of c.
