Let g(t) = est. a. Solve the initial value problem y - 8y = g(t), y(0) = 0, using the technique of integrating factors. (Do not use Laplace transforms.) y(t) = b. Use Laplace transforms to determine the transfer function p(t) given the initial value problem p' 80 = 8(1), (0) = 0. (t) = c. Evaluate the convolution integral (o * g)(t) = J p(t w) g(w) dw, and compare the resulting function with the solution obtained in part (a). (p * g)(t) = . dw =