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