\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( v+2 \right ) \left ( v-1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.015002 (sec), leaf count = 30 \[ \left \{\left \{y(x)\to c_1 \left (x^2-1\right ) P_v^2(x)+c_2 \left (x^2-1\right ) Q_v^2(x)\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( x-1 \right ) \left ( 1 +x \right ) {\it LegendreP} \left ( v,2,x \right ) +{\it \_C2}\, \left ( x -1 \right ) \left ( 1+x \right ) {\it LegendreQ} \left ( v,2,x \right ) \right \} \]