xy'' -(2x+1)y' + (x+1)y = (x e(adsbygoogle = window.adsbygoogle || []).push({}); ^{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.

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# Could use a little advice here, with a 2nd order ODE

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