\[ y''(x)=\frac {2 (2 a-1) x y'(x)}{x^2-1}-\frac {y(x) \left (x^2 (2 a (2 a-1)-v (v+1))+2 a+v (v+1)\right )}{\left (x^2-1\right )^2} \] ✓ Mathematica : cpu = 0.0390137 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \left (x^2-1\right )^a \left (c_1 P_v(x)+c_2 Q_v(x)\right )\right \}\right \}\]
✓ Maple : cpu = 0.06 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{a} \left ( {\it LegendreQ} \left ( v,x \right ) {\it \_C2}+{\it LegendreP} \left ( v,x \right ) {\it \_C1} \right ) \right \} \]