Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y"-5y6(t-3). v(0)-3, 1/(0) - 0. a Find the Laplace transform of the solution Y(s)=L(u(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 3. If 0 < t < 3, y(t). if 3 < t < 0. 4