\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\, \left ( v-1 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,vy \left ( x \right ) =0} \]
Mathematica: cpu = 0.021003 (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 = 0.094 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{v }+{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{v}x {\mbox {$_2$F$_1$}({\frac {1}{2}},v+1;\,{\frac {3}{2}};\,{x}^{2})} \right \} \]