The question goes...

Find the general solution of this differential equation, given that a solution of the corresponding homogeneous equation is $\displaystyle y=x$,

$\displaystyle x^2y''+x(x-2)y'-(x-2)y=x^3$

I've checked that $\displaystyle y=x$ is a solution when the equation has a 0 on the RHS, but it's the whole setting $\displaystyle y(x)=u(x)v(x)$ thing I'm stuck with. Obviously that's $\displaystyle y(x)=xv(x)$, but from there I'm stuck. Can anyone help?