- #1

helpppmeee

- 15

- 0

## Homework Statement

y'' + y = xsinx where y(0) = 0 and y'(0) = 1

## Homework Equations

yc = C1sinx + C2cosx

## The Attempt at a Solution

So my attempt includes the yc which undoubtedly is correct. I now try to solve yp

yp = Axsinx + Bxcosx

y''p = A(2cosx - xsinx) + B(-2sinx - xcosx)

Substituting: y''p + yp = xsinx, clearly doesn't equal xsinx. There are no comparable values to xsinx to even try and solve for A or B.

Attempting using a different algorithm: yp = (A + Ax)sinx + (B + Bx)cosx

Notice overlap from yp to yc, therefore multiply by x: yp = (Ax +Ax^2)sinx + (Bx + Bx^2)cosx

y''p = A(2cosx + 2sinx -xsinx +4xcosx -x^2sinx) + B(-2sinx + 2cosx - 4xsinx - x^2cosx)

and y''p + yp = A(2cosx + 2sinx + 4xcosx + xsinx) + B(-2sinx + 2cosx - 4xsinx + xcosx)

Arrgggh this is really troubling me. I honestly have no idea what I'm doing wrong or how to proceed with the Initial Value Problem afterwards.