HWOB: Problem 12 (1 point] We consider the nonhomogeneous initialyalue problem 22y + Smy' + 101: = 2643a, y{1] = 8, 1(1) 2 1 By looking for

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HWOB: Problem 12 (1 point]We consider the non—homogeneous initialyalue problem 22y" + Smy’ + 101: = 2643a, y{1] = 8, 1(1) 2 —1 By looking for solutions in the form y = 3' in the homogeneous Euler—Cauchy problem fizzy” + 3314’ + Cy = 0, we obtain a auxiliaryequation Ar: + {B — A}? + C = I] which is the analog ofthe auxiliary equation in the constant coefficient case. (1} For this problem find the auxiliary equation: = 0(2) Find the roots ofthe auxiliary equation: (enter your results as a comma separated list )(3} Find a fundamental set of solutions yhyg: (enter your results as a comma separated list J. Then the complementary solution is yc 2 mm + 623,13. (4) For the non—homogeneous problem we need to apply the variation of parameters formula to find a particular solution yr. Carrying this outyou obtain yP 2Recall that the general solution is y 2 ya + 11?. Find the unique solution satisfying 9(1) 2 8, y'fl) = —1 y: