1. (10 points) Use the method of undetermined coefficients to find the solution of the initial value problem y" ty =5x2e20 y(0) = 1, y'(0) = 0. 2. (10 points) Use the method of undetermined coefficients to determine the general solution to y" (t) + y(t) = 2t cost. 3. Use the method of variation of parameters to find the general solutions of the following differ- ential equations. (a) (5 points) y" ty = tan x sec x, 2 (b) (5 points) y" + 4y' + 4y = e-"" Inx, x> 0