Solve the following differential equation using the method of undetermined coefficient coefficients

d^2y/dx^2 + 9y = x^2 cos3x

This was the most difficult assignments i had encounted as this was not taught in our module yet we are required to solve it . what i had learn before are the right hand side x^2 + cos3x but not multiply .

r^2 + 9 = 0

r(r+ 9) = 0

r=+/- 3j

Yc =C1cos3x + C2sin3x

Yp= (Ax^2 + Bx + C) (Dcos3x + Esin3x) ?