After simplifying the vortex equation, I get to this equation:
$$ -\alpha y \partial_y \omega = \alpha \omega + \nu \partial_{yy} \omega $$
where the $\alpha$ and $\nu$ are constant values and $\omega(y)$. I want to solve the equation for $\omega(y)$. How can I do it? I appreciate in advance for kind helps.
Regards,
Ehsan