I have the following equation
$$\frac{d}{dx} \bigg( \frac{1}{(1+ x^2)^2} \frac{dy}{dx} \bigg) + \lambda x^2 y =0 \ .$$
I'm trying to re-write it so that it looks more like a physically relevant equation:
$$ -\frac{d^2 \psi}{dx^2} - i V_1 (x) \frac{d \psi}{d x} + V_2 (x) \psi = \lambda \psi $$
I think you can do this by multiplying the equation by some function $f(x)$ and and then doing a change of coordinates and re-defining the wave function as $\psi (x) = f(x) y(x)$, but what should $f$, $V_1$ and $V_2$ be in order to do this?