- #1

- 45

- 0

## Main Question or Discussion Point

xy'' -(2x+1)y' + (x+1)y = (x e

I know a solution - (x-1)e

Thus, y= ((x-1)e

Now, i know how to do the whole reduction of order thing, but when i find y' and y'' and substitute, the u(x) term doesn't cancel out so this doesn't work

(x

So, how do i approach this? Thanks.

^{x})^{2}I know a solution - (x-1)e

^{2x}Thus, y= ((x-1)e

^{2x}u(x))Now, i know how to do the whole reduction of order thing, but when i find y' and y'' and substitute, the u(x) term doesn't cancel out so this doesn't work

(x

^{2}-x)u'' + (2x^{2}-x+1)u' + x^{2}u = x^{2}So, how do i approach this? Thanks.