\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-2\,{\frac {x \left ( n+1-2\,a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{2}-1}}-{\frac { \left ( 4\,a{x}^{2} \left ( a-n \right ) - \left ( {x}^{2}-1 \right ) \left ( 2\,a+ \left ( v-n \right ) \left ( v+n+1 \right ) \right ) \right ) y \left ( x \right ) }{ \left ( {x}^{2}-1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.051506 (sec), leaf count = 54 \[ \left \{\left \{y(x)\to c_1 \left (x^2-1\right )^{\frac {1}{2} (2 a-n)} P_v^n(x)+c_2 \left (x^2-1\right )^{\frac {1}{2} (2 a-n)} Q_v^n(x)\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}-1 \right ) ^{a -{\frac {n}{2}}}{\it LegendreP} \left ( v,n,x \right ) +{\it \_C2}\, \left ( {x}^{2}-1 \right ) ^{a-{\frac {n}{2}}}{\it LegendreQ} \left ( v, n,x \right ) \right \} \]