Loops Assignments HW8: Problem 18 US List Next (1 point) We consider the non-homogeneous problem y"-y' =-30 cos(3x) First we consider the homogeneous problem y"-y' = 0 1) the auxiliary equation is art br + c = 2) The roots of the auxiliary equation are 3) A fundamental set of solutions is the complementary solution ye = qy + c2y2 for arbitrary constants C1 and C2 . =0. (enter answers as a comma separated list) (enter answers as a comma separated list). Using these we obtain the Next we seek a particular solution yp undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find y = 1 + 2 and a particular solution: We then find the general solution as a sum of the complementary solution y = y, + y' Finally you are asked to use the general solution to solve an MP. q 5) Given the initial conditions y(0) = 1 and y/ (0) = 3 find the unique solution to the IVP