Solve ODEs

(a) (b) (C) (d) (f) Find the particular solution for the unknown y(a:): I %+2y=1m2, y(0)=0. Find the particular solution for the unknown y(:1:): y\" + 4y = 0, MO) = EN) = 1. Find the particular solution for the unknown y(:1:): y\" + 4y\" = 1, 31(0) = y'(0) = 0. Find the general solution for the unknown y(m): y"|-y' 23; = em by the method of Variation of Parameters. Find the general solution for the unknown y(m): y\" _ y = a: for a: 6 [7r, 7r] using Fourier series. Find the particular solution for the unknown y(x): y\" y = sinsc, y(0) = 03910): 0 using Laplace Transform