Consider the Volterra integral equation (see 16) (t) + _ t 0 (t ) () d = sin(2t). (30)

QUESTION:

Consider the Volterra integral equation (see 16) (t) + _ t 0 (t ) () d = sin(2t). (30) a. Solve the integral equation (30) by using the Laplace transform. b. By differentiating equation (30) twice, show that (t) satisfies the differential equation __(t) + (t) = 4 sin(2t). Show also that the initial conditions are (0) = 0, _(0) = 2. c. Solve the initial value problem in part b, and verify that the solution is the same as the one in part a. 1