I have to solve (analytically) an ODE for $x \in ]0,1[$: $$x(1-x)\frac{d^2}{dx^2}u+(1+2δ-2δx)\frac{d}{dx}u+(δ-α+αx)u=0,$$ where $α$ and $δ$ constants. This is similar to Baer equation and to Mathieu as well, but I could not find one of both cases for the equation above. (Tried lot of different manipulations on $x$ or $u$ unsuccessfully).
When $α =0$ this is the hypergeometric differential equation (not the case here).
Could anyone give a hint?
Maple says the solutions are $$u \left( x \right) =c_{{1}}{\it HeunC} \left( 0,2\,\delta,-2,-\alpha,1 +\alpha,x \right) +c_{{2}}{x}^{-2\,\delta}{\it HeunC} \left( 0,-2\, \delta,-2,-\alpha,1+\alpha,x \right) $$