HW8: Problem 13 Previous Problem ListNext (1 point) We consider the non-homogeneous problem y" +2y +2y - 20 sin(2x) First we consider the homogeneous problem y" + 2y + 2y = 0 : 1) the auxiliary equation is ar2 + br + c = 2) The roots of the auxiliary equation are 3) A fundamental set of solutions is the complementary solution ye = cin + c2y2 for arbitrary constants c' (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the and e- Next we seek a particular solution y of the non-homogeneous problemy" + 2y + 2y = 20 sin(2x) using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find We then find the general solution as a sum of the complementary solution ye ciyi +c2)2 and a particular solution: y ye typ Finally you are asked to use the general solution to solve an IVP 5) Given the initial conditions y(0)--3 andy (0-3 find the unique solution to the IVP 26