Problem 3. (40 points): Solve the following initial value problem using Laplace transform:
(a) \(t \frac{d^2y}{dt^2} + \frac{dy}{dt} + ty = 0\), \(t > 0\), \(y(0) = 1\), \(y'(0) \neq 0\)
(b) \(\frac{d^2y}{dt^2} + t \frac{dy}{dt} + y = 0\), \(t > 0\), \(y(0) = 1\), \(y'(0) = 0\)