Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. ?" + 9my = 3nd(t - 5), y(0) =0, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = Cty(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. if 0