I am trying to solve the following second-order DE: $$ y^{\prime\prime}(x)+\left(\frac{1}{x-9}+\frac{1}{x-1}+\frac{1}{x}\right)y^{\prime}(x)+ \left(\frac{1}{12(x-9)}+\frac{1}{4(x-1)}-\frac{1}{3x}\right)=0$$ I know that the solution is $$ \frac{4\, K\left(\frac{16\sqrt{x}}{(\sqrt{x}-1)^3(\sqrt{x}+3)}\right)}{\sqrt{(\sqrt{x}-1)^3(\sqrt{x}+3)}} $$ where K(m) is the elliptic integral of the first kind. Usually it is the solution of a second-order DE with only three regular singular points, but the DE above has four singular points.
Does someone know a way to derive the given solution from the DE, e.g. by removing one of the singular points?
I also tried changing variables to $x=y^2$ but this introduces more singular points.