\[ -(-n+v+1) (n+v) y(x)-2 (n-1) x y'(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0234265 (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 = 0.053 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{{\frac {n}{2}}}{\it LegendreP} \left ( v,n,x \right ) +{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{{\frac {n}{2}}}{\it LegendreQ} \left ( v,n,x \right ) \right \} \]