Finding a weighting function

Question

I have this equation: $$(1+x)y''-xy'-y = 2x.$$ I have to bring this equation to the self-adjoint form. I have already solved this step with using integration factor method and I obtained, \begin{equation} [(x+1)e^{-x}y']'-e^{-x}y = 2x(x+1)e^{-x} \end{equation} but my problem is that from here I don't know how can i find the $p(x),\rho(x)$ and $q(x)$ from the self-adjoint form so that i can then solve the differential equation using Lagrange? so all i need is to know how can i extract them from the self-adjoint equation found. Thanks in advance.