(1 point) We consider the initial value problem x2y" + 9xy' + 25y = 0, y(1) = 2, y' (1) = -14 By looking for solutions in the form y = x" in an Euler-Cauchy problem Axy" + Bxy' + Cy = 0, we obtain a auxiliary equation Ar2 + (B - A)r + C = 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list ) (3) Find a fundamental set of solutions y1 , y2 : (enter your results as a comma separated list ) (4) Recall that the complementary solution (i.e., the general solution) is y. = CIy1 + C212 . Find the unique solution satisfying y(1) = 2, y' (1) = -14 y =(1 point) We consider the initial value problem 9x2 y" + 9xy' + 16y = 0, y(1) = 3, y' (1) = -8 By looking for solutions in the form y = x" in an Euler-Cauchy problem Ax2y" + Bxy' + Cy = 0, we obtain a auxiliary equation Ar2 + (B - A)r + C = 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list ) (3) Find a fundamental set of solutions y1 , y2 : (enter your results as a comma separated list ) (4) Recall that the complementary solution (i.e., the general solution) is y. = CIy1 + C212 . Find the unique solution satisfying y(1) = 3, y' (1) = -8 y =