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