HW3 2023: Problem 4 (8 points) In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y6y+9y=927t12te3t with initial values y(0)=3 and y(0)=7 A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.) B. Write the fundamental solutions for the associated homogeneous equation. y1= C. Write the form of the particular solution and its derivatives. (Use A,B,C, etc. for undetermined coefficients. Y=Y=Y= D. Write the general solution. (Use c1 and c2 for c1 and c2 ). y= E. Plug in the initial values and solve for c1 and c2 to find the solution to the initial value problem. y= Hint: No fractions are required in the solution or answer to this