Q2(a) Compute the inverse Laplace transform then sketch a graph of the following function: ?(?) = 1 ? 2 (1 ? ? ?? ) 2 (8 marks) (b) Solve the differential equation using Laplace transform and inverse Laplace transform: ??? + 4? = ? ?? ?(0) = 2; ?'(0) = 1 (12 marks)

Q2(a) Compute the inverse Laplace transform then sketch a graph of the following function: 1 f(t) = 2(1-e-5)2 (8 marks) (b) Solve the differential equation using Laplace transform and inverse Laplace transform: y" + 4y = ert y(0) = 2; y'(0) = 1 (12 marks)