Question: (1 point) We consider the initial value problem 12x2y - 15xy' + 6y = 0, y(1) = 2, y' (1) = -2 By looking for

(1 point) We consider the initial value problem 12x2y" - 15xy' + 6y = 0, y(1) = 2, y' (1) = -2 By looking for solutions in the form y = x" in an Euler-Cauchy problem Axzy" + 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) = -2 y =(1 point) We consider the initial value problem x2)!\" 6y = 0, y(1) = 2, 3/ (1) = 3 By looking for solutions in the form y = x" in an Euler-Cauchy problem 113:2 y\" + 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 nd 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 M , y2 : (enter your results as a comma separated list) (4) Recall that the complementary solution (i.e., the general solution) is ya = 013'1 + czyz. Find the unique solution satisfying 37(1) = 2, 3/(1) = 3 y: (1 point) We consider the initial value problem 4x2y\" - 3xy' + 3y = 0, y(1) = 2, 3/0) = -3 By looking for solutions in the form y = x' in an Euler-Cauchy problem Ax2 y\" + 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 nd 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 yl , yz : (enter your results as a comma separated list) (4) Recall that the complementary solution (i.e., the general solution) is yc = clyl + CzYz- Find the unique solution satisfying y(]) = 2, 3/(1) = 3 y

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