Hello all,

I want to show that a function $\displaystyle w$ is a solution to Hermite's equation

$\displaystyle \frac{d^{2}w}{dx^{2}}-2x\frac{dw}{dx}+2\ell w =0$

if and only if $\displaystyle w$ is a solution to the Sturm-Liouville equation

$\displaystyle \left( e^{-x^{2}}w' \right)'+2\ell e^{-x^{2}}w=0$

Could someone assist me in the right direction.

Thanks.