(2 points) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y\" + 42:2 y = 27:50 3), y(0) = 0, y'(()) = 0. a. Find the Laplace transform of the solution. Y(S) = {y(t)} = b. Obtain the solution y(t). Use h(t) to denote any step functions. y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 3. y(t)= if0$t