[25 points} In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y' + y' + 9y = 6re-3r 49-?\" + 9: + 24 with initial values y(0) = 5 and fat) = 7_ A. Write the characteristic equation for the associated homogeneous equation. (Use 2: for your variable.) B. 1u'lirite the fundamental solutions for the associated homogeneous equation. 3'1 = 3'2 = 0. Write the form ofthe particular solution and its derivatives. (Use A. B. C, etc. for undetermined coefficients. Y: Y! 1;\" D. Write the general solution. (Use cl and :22 for c. and cl). 3.! : E. Plug in the initial values and solve for c] and C2 to 1in the solution to the initial value problem. 3,): Hint: No fractions are required in the solution or answer to this