I have a problem of the form
$$ \left\{ \begin{array}{l} Q_1(x) = \frac{1}{x^2+1} && \\ \left(a_k(x) + b_k(x)\frac{d}{dx}\right)Q_k(x) = Q_{k+1}(x) && k \geq 1 \end{array} \right. $$
Are problem like this studied somewhere? For example I would be interested in a closed form expression for $Q_k(x)$.
I realize I'm being generic, but I just need some reference if there's any.