\[
\boxed{
{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) =2\,{\frac {x \left( 2\,a-1 \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) }{{x}^{2}-1}}-{\frac { \left( {x}^{2} \left( 2\,a \left( 2\,a-1 \right) -v \left( v+1 \right)  \right) +2\,a+v \left( v+1 \right)  \right) y \left( x \right) }{ \left( {x}^{2}-1 \right) ^{2}}}=0}
\]