Set up but do not solve for the appropriate particular solution yp for the differential equation
using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).
The Attempt at a Solution
I first solved the associated homogeneous equation and got the equation r^2+25r=0 and the roots are 0 and -5. So the equation becomes C1+C2e^(-5x).
I separated 2x as (Ax+B) then seeing as it's being multiplied by sin (5x), I can just do (Ax+B)cos(5x)+(Cx+D)sin(5x). I check this solution with my homogeneous and there are no repeated terms. I tried entering this solution in (Ax+B)cos(5x)+(Cx+D)sin(5x and it keeps telling me I'm wrong. Am I doing something wrong or forgetting a step or two?
Am I doing something horrificly wrong?