solve the ODE using laplace transform

A simple ICI'EIIE example and an Engineering problem... 1. Solve the CIDE y"+y'-2y= y[0}=y'(}=1 using the method of trial solution 3; = em like in the second year differential equations course, and also using the Laplace transform method. 2. {A} The Laplace transform of a periodic function t} with period T is given by H T cssn=% where 1115):] erred: {1 2-33)? 5 Suppose f[t} is a periodic function with period 6 such that 15(5) = . Use this Ffs} to show that 1 - e4\" {f{1}}= m {B} Let f[t]l he the function of part [A] 1whose Laplace transform is given above. Suppose Ys} is the Laplace transform of the solution to the initial value problem y'if}=1f(t} with y(} =n Find an expression for Y[s]