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