Given the following differential equation: y" + y=t a) Perform Laplace Transform to the differential equation [5 marks] b) If the initial values are y(0)=1 and y'(0) = -2, show that F(s) = 1 S 2 + s² (s²+1) s² + 1 [5 marks] c) For the F(s) in part (b), find its inverse Laplace transform, f(t) as the solution of the differential equation [10 marks]
