- #1

Chemmjr18

- 51

- 1

## Homework Statement

Find a particular solution yp of the given equation:

y''+y=sinx+xcosx

## Homework Equations

## The Attempt at a Solution

1) First I got the temporary y

_{p}: Asinx+Bcosx+(Cx+D)sinx+(Ex+F)cosx

2) Then I got the associated homogenous eq. check for to check for duplicates: C

_{1}cosx+C

_{2}sinx

3) Since there were duplicates, I multiplied the temporary solution by x: Axsinx+Bxcosx+(Cx

^{2}+Dx)sinx+(Ex

^{2}+Fx)cosx

4) I obtained the 2nd derivative of this and refined it: (2A+2C+2F)cosx+(-2B-2D+2E)sinx+(4E-D-B)xcosx+(-A-4C-F)xsinx-Cx

^{2}cosx-Ex

^{2}sinx

5) I then added this to 2) to get (2A+2C+2F)cosx+(-2B-2D+2E)sinx+(4E)xcosx+(-4C)xsinx=sinx+xcosx

I have more unknowns than I do equations, so I can't solve. Where'd I go wrong? I've been combing through the problem for almost 4 hours...