\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -v \left ( v+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.017002 (sec), leaf count = 18 \[ \left \{\left \{y(x)\to c_1 P_v(x)+c_2 Q_v(x)\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 15 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it LegendreP} \left ( v,x \right ) +{\it \_C2}\,{\it LegendreQ} \left ( v,x \right ) \right \} \]