\[ y''(x)=-(v-n) (n+v+1) y(x)-(2 n+1) \cot (x) y'(x) \] ✓ Mathematica : cpu = 0.143888 (sec), leaf count = 46
\[\left \{\left \{y(x)\to c_1 \left (\cos ^2(x)-1\right )^{-n/2} P_v^n(\cos (x))+c_2 \left (\cos ^2(x)-1\right )^{-n/2} Q_v^n(\cos (x))\right \}\right \}\] ✓ Maple : cpu = 0.666 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) = \left ( \sin \left ( x \right ) \right ) ^{-n} \left ( {\it LegendreQ} \left ( v,n,\cos \left ( x \right ) \right ) {\it \_C2}+{\it LegendreP} \left ( v,n,\cos \left ( x \right ) \right ) {\it \_C1} \right ) \right \} \]