This is the equation:
$$x^2 (x-5)^2y''+4xy'+(x^2-25)y=0$$
My problem is that I didn't know what to do with $(x-5)^2$, if I divided the equation by this value, it will no longer be Bessel's equation.
Any suggestions or help?
is it possible to find the indical equation using the usual fomula $$r^2+[P(0)-1]+Q(0)=0$$ , or since its not bessel i cant use it ?
It's not Bessel's equation. Maple solves it using Heun functions. $$y \! \left(x \right) = c_{1} x^{\frac{21}{50}+\frac{\sqrt{2941}}{50}} \left(x -5\right)^{\frac{2}{25}-\frac{\sqrt{2941}}{50}-\frac{i \sqrt{3}}{2}} \mathit{HeunC}\! \left(\frac{4}{25}, i \sqrt{3}, \frac{\sqrt{2941}}{25}, -\frac{108}{625}, \frac{1}{2}, -\frac{5}{x -5}\right)+c_{2} x^{\frac{21}{50}+\frac{\sqrt{2941}}{50}} \left(x -5\right)^{\frac{2}{25}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{2941}}{50}} \mathit{HeunC}\! \left(\frac{4}{25}, -i \sqrt{3}, \frac{\sqrt{2941}}{25}, -\frac{108}{625}, \frac{1}{2}, -\frac{5}{x -5}\right) $$
If you're looking for series solutions, you might start by finding the indicial equation.