\[ y''(x)=\frac {2 (2 a-1) x y'(x)}{x^2-1}-\frac {y(x) \left (x^2 (2 a (2 a-1)-v (v+1))+2 a+v (v+1)\right )}{\left (x^2-1\right )^2} \] ✓ Mathematica : cpu = 0.0435448 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right )^a P_v(x)+c_2 \left (x^2-1\right )^a Q_v(x)\right \}\right \}\]
✓ Maple : cpu = 0.057 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{a}{\it LegendreP} \left ( v,x \right ) +{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{a}{\it LegendreQ} \left ( v,x \right ) \right \} \]