\[ -2 (v-1) x y'(x)-2 v y(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0218762 (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 = 0.16 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{v}+{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{v}x{\mbox {$_2$F$_1$}({\frac {1}{2}},v+1;\,{\frac {3}{2}};\,{x}^{2})} \right \} \]