Answer: Consider the Volterra integral equation (see 21) (t) + t 0 (t )() d = sin 2t
Chapter 6, Problem 22(choose chapter or problem)
Consider the Volterra integral equation (see 21) (t) + t 0 (t )() d = sin 2t. (i) (a) Solve the integral equation (i) by using the Laplace transform. (b) By differentiating Eq. (i) 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).
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