# Math Help - x^2 φ'' (x)+xφ' (x)-λφ(x)=0

1. ## x^2 φ'' (x)+xφ' (x)-λφ(x)=0

$x^2 \varphi'' (x)+x\varphi' (x)-\lambda\varphi(x)=0$

How is this DE solved?

This is a separation from PDE. I don't know what to do at this point.

2. Originally Posted by dwsmith
$x^2 \varphi'' (x)+x\varphi' (x)-\lambda\varphi(x)=0$

How is this DE solved?

This is a separation from PDE. I don't know what to do at this point.
It's a Cauchy-Euler equation. You assume that the solution is of the form $\varphi(x)=x^r$. Thus, the characteristic equation for the ODE in question is $r^2-\lambda=0$.

I'm sure you can finish this off.