\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\, \left ( n+1 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( v+n+1 \right ) \left ( v-n \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.026003 (sec), leaf count = 42 \[ \left \{\left \{y(x)\to c_1 \left (x^2-1\right )^{-n/2} P_v^n(x)+c_2 \left (x^2-1\right )^{-n/2} Q_v^n(x)\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{- {\frac {n}{2}}}{\it LegendreP} \left ( v,n,x \right ) +{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{-{\frac {n}{2}}}{\it LegendreQ} \left ( v,n ,x \right ) \right \} \]