\[ y''(x)=-\frac {y(x) \left (4 a x^2 (a-n)-\left (x^2-1\right ) (2 a+(v-n) (n+v+1))\right )}{\left (x^2-1\right )^2}-\frac {2 x (-2 a+n+1) y'(x)}{x^2-1} \] ✓ Mathematica : cpu = 0.0333893 (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 = 0.277 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{a-{\frac {n}{2}}} \left ( {\it LegendreQ} \left ( v,n,x \right ) {\it \_C2}+{\it LegendreP} \left ( v,n,x \right ) {\it \_C1} \right ) \right \} \]