I'm trying to transform the following differential equation $$\frac{\sigma^2}{2}x^2y''+(1-rx)y'-\lambda y=0$$ Into a Kummer differential equation, so something of the form: $$ xf''(x)+(b-z)f'(x)-af(x)=0. $$ From reading some other posts I tried using $y=x^af(x)$, but it didn't work, or at least I couldn't get it to work.
Any suggestions would be welcomed.
Edit. I'm reffering to this post Kummer solution to second order ODE : what I can't get is to have $xf''$ without having a $\frac{1}{x}f'(x)$ term