\[ -2 (v-1) x y'(x)-2 v y(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0153973 (sec), leaf count = 42
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right )^{v/2} P_v^v(x)+c_2 \left (x^2-1\right )^{v/2} Q_v^v(x)\right \}\right \}\] ✓ Maple : cpu = 0.224 (sec), leaf count = 28
\[\left \{y \left (x \right ) = \left (c_{2} x \hypergeom \left (\left [\frac {1}{2}, v +1\right ], \left [\frac {3}{2}\right ], x^{2}\right )+c_{1}\right ) \left (x^{2}-1\right )^{v}\right \}\]