Could you please help me with # 1(b,d,f), 2(a,c)? I am very confused on how to do these problems and need a lot of help.

1. Use the Laplace transform to find the solution of the IVP. a) 2y' ty = 1, y(0) = 2 b) 3y' = -ytet, y(0) = = c) y" +y' - 2y =0, y(0) = 0, y'(0) = -1 d) y" - 6y' + 9y =0, y(0) = 0, y'(0) = 2 e) 5y" - y' =0, y(0) = -1, y'(0) = -1 f) 4y" +y =0, y(0) = -1, y'(0) = -1 g) y" - 2y' + 2y =0, y(0) = -1, y'(0) = -1 h) y" + 2y' + 5y =0, y(0) = 0, y'(0) = -6 2. Use the Laplace transform to find the solution of the IVP. a) y" + y' - 2y = 12t, y(0) = 0, y'(0) = 0 b) y" + 4y = 8t2, y(0) = 0, y'(0) = 0 c) y" - y' = 2 sint, y(0) = 0, y'(0) = 0 d) y" + 3y' = 3t + 1, y(0) = 0, y'(0) = 0 e) y" - 2y' + 5y =5-4e-t, y(0) = 0, y'(0) = 0