\[ y''(x)=-\frac {y(x) \left (4 a x^2 (a-n)-\left (x^2-1\right ) (2 a+(v-n) (n+v+1))\right )}{\left (x^2-1\right )^2}-\frac {2 x (-2 a+n+1) y'(x)}{x^2-1} \] ✓ Mathematica : cpu = 0.0622388 (sec), leaf count = 54
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right )^{\frac {1}{2} (2 a-n)} P_v^n(x)+c_2 \left (x^2-1\right )^{\frac {1}{2} (2 a-n)} Q_v^n(x)\right \}\right \}\]
✓ Maple : cpu = 0.069 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{a-{\frac {n}{2}}}{\it LegendreP} \left ( v,n,x \right ) +{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{a-{\frac {n}{2}}}{\it LegendreQ} \left ( v,n,x \right ) \right \} \]