Integral transform methods for solving ODES a. Solve y" + 2y' +y f(t) with y(0) y'(0) = 0, where f(t) = 1 for 0 < t < a and f(t) = 0 for t > a. Find the Green's function for the problem and use it to obtain the solution y(t) for t a. b. Solve y" + 4y" - 5y' 0 with initial conditions y"(0) 23;y'(0) = -7; y(0) = 4 %3!