\[ y''(x)=\frac {2 (2 a-1) x y'(x)}{x^2-1}-\frac {y(x) \left (x^2 (2 a (2 a-1)-v (v+1))+2 a+v (v+1)\right )}{\left (x^2-1\right )^2} \] ✓ Mathematica : cpu = 0.0288032 (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 = 0.051 (sec), leaf count = 23
\[y \relax (x ) = \left (x^{2}-1\right )^{a} \left (c_{1} \LegendreP \left (v , x\right )+c_{2} \LegendreQ \left (v , x\right )\right )\]