\[ -2 (v-1) x y'(x)-2 v y(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0216133 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \left (x^2-1\right )^{v/2} \left (c_1 P_v^v(x)+c_2 Q_v^v(x)\right )\right \}\right \}\]
✓ Maple : cpu = 0.186 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{v} \left ( {\mbox {$_2$F$_1$}({\frac {1}{2}},v+1;\,{\frac {3}{2}};\,{x}^{2})}{\it \_C2}\,x+{\it \_C1} \right ) \right \} \]