Homework help

Problem 1: Consider the IVP y" + 4y = sin(2t), y(0) = 1, y'(0) = 0. (a) Find the solution by using the method of undetermined coefficients. (b) Find the solution by using the method of variation of parameters. In both cases, you need to provide all the details of your calculations.Problem 2: (a) Calculate Citcos(at)} (s). (b) Write ramp in terms of C{sin(at)}(s) and the expression in (a). (c) Using (b), solve the IVP from Problem 1 by using the method of Laplace transform. (d) Compare the three approaches in Problems 1 and 2. Which one did you find the easiest? Which the hardest? Why? You need to provide all the details of your calculations