# Undetermined Coefficients

## Homework Statement

Set up but do not solve for the appropriate particular solution yp for the differential equation
y''+25y=2xsin(5x)
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?

Last edited:

vela
Staff Emeritus
Homework Helper
One of your roots is wrong. It should be -25, not -5. Other than that, it looks good so far.

Yeah sorry, I was missing the first half of the question, if it says setup but don't solve for the coefficients for just the particular solution, is what I have correct because it keeps saying i'm wrong and I have no idea. Am I missing some steps?

vela
Staff Emeritus
oh ****.. yeah it's 25y.. but how does it change my particular solution? 