Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function;
y" - 4y' = delta(t - 5),
y(0) = 2, y'(0) = 0.
a. Find the Laplace transform of the solution:
Y(s) = L{y(t)}
b. Obtain the solution y(t):
y(t)
c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 5
y(t) = {
if 0 <= t < 5,
if 5 <= t < infinity.
