I would like to transform
$$0 = D u P''(u) - (D+G u)P'(u) + (G-Vu)P(u)$$
into a common differential equation. It's my understanding that since this equation has less than three regular singular points ($u = 0$ and $u=\infty$?), my equation should transform into the Hypergeometric differential equation:
$$ z(1-z)y''(z) + [c-(a+b+1)z]y'(z) -a b y(z) = 0 $$ for a suitably chosen $y$ and $z$.
Is there any systematic means by which I can find the correct transformation between my variables $P$ and $u$ and the standard form variables $y$ and $z$?