## Sturm Liouville Problem

Problem: find the eigenvectors and eigenfunctions of the following Sturm-Liouville problem:

$
\frac{d}{dx} \left(x^4 \frac{dy}{dx} \right) + \lambda yx^2 = 0,
$

Since $
x \neq 0
$
i can rearrange to

$
\displaystyle
x^4 \frac{d^2 y}{dx^2} + 4x^3 \frac{dy}{dx} + \lambda yx^2 = 0
$

When substituting $
y = x^k
$
i am having difficulties when simplifying to get k on its own.
Am i doing this correctly?