I am looking at a 2nd order ODE:
\begin{equation} \frac{d^2u}{dx^2} + p(x)\frac{du}{dx} + q(x) u = 0 . \end{equation}
that has five regular singular points: say at $0$, $1$, $a$, $b$, and $\infty$, where $a$ and $b$ are real numbers. I suspect I can ``factor out'' one singularity of the equation (as is done for example for another equation here), and thus transform this equation into a Heun equation. Is there a general way/theory/procedure to determine when one can factor out a singularity for a given ode? I'd greatly appreciate a simple demonstration, example, or references to the literature on this subject.