\[ -2 (v-1) x y'(x)-2 v y(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0145356 (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 = 0.504 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{v} \left ( {\mbox {$_2$F$_1$}({\frac {1}{2}},v+1;\,{\frac {3}{2}};\,{x}^{2})}{\it \_C2}\,x+{\it \_C1} \right ) \right \} \]