I posted this on mathstack and it is not a homework problem, I am doing a modeling problem and this ODE comes up. I don't know whether it could be considered to be a research problem yet. Please help me to close it if it is not placed at the right place.

I have a problem with finding the closed form solution of the following ODEs. I am NOT sure that a closed form solution exists. Closed form here means that the solution can be presented as integrals/ power series. Here is the ODE : I only consider $x\in (0,1)$ and $c_i$ are known non-zero real numbers.

$y''(x) + [\frac{c_1}{x^2}+\frac{c_2}{(1-x)^2} +c_3(\frac{1}{x}+\frac{1}{1-x})]y'(x)+[c_4(\frac{1}{x}+\frac{1}{1-x})+\frac{c_5}{x^2}+\frac{c_6}{(1-x)^2}]y(x)=0 $

I can find the solution inform of power series which is very ugly. I would like to ask you all that whether you can give a method that can be used to find the solution in a nicer way. Thanks so much for your time. I really appreciate it.