.J l. Question 2 7 pts Given the differential equation y" + 4y' + 13y = 0. Do Not add any SPACES in your answer. a) The associated auxiliary equation of the differential equation is. b) Solve the differential equation. c) Solve the initial value problem with the differential equation with the conditions y(0) = 5 and y'(0) = 41. The c-values found in part (c) are and 33* Question 3 6 pts Given set of functions f1(x) = x'1, f2(x) = 3x2 - 2x Do Not add any SPACES in your answer. a) Find the Wronskian of the functions. b) Find the largest interval that the set of functions is linearly independent. Question 4 7 pts The given two-parameter family y = c1x4 + c2x2 - 2 is a solution of the differential equation x2y" - 4xy' + 3y = 20 on the interval (-infinity, infinity). Determine whether a member of the family can be found that satisfies the boundary conditions y(0) = -2 and y(1) = 5 . Rewrite the solution in terms of one constant value if possible