Q2(a) Solve the differential equation using Laplace transform Y(s) and inverse Laplace transform, y(t). y +...

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Q2(a) Solve the differential equation using Laplace transform Y(s) and inverse Laplace transform, y(t). y" + y = cost + cos(t – n) sin(t – n), y(0) = 2 and y'(0) = 1 (10 marks) (b) Given the function: x(3 + x) - 3 <x < 0 f(x) = 3x – x2 0 <x < 3 Demonstrate the Fourier series of f(x) function. (10 marks) Q2(a) Solve the differential equation using Laplace transform Y(s) and inverse Laplace transform, y(t). y" + y = cost + cos(t – n) sin(t – n), y(0) = 2 and y'(0) = 1 (10 marks) (b) Given the function: x(3 + x) - 3 <x < 0 f(x) = 3x – x2 0 <x < 3 Demonstrate the Fourier series of f(x) function. (10 marks)