\[ y''(x)=(n-v) (n+v+1) y(x)-(2 n+1) \cot (x) y'(x) \] ✓ Mathematica : cpu = 0.181214 (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 = 0.19 (sec), leaf count = 26
\[\{y \left (x \right ) = \left (c_{1} \LegendreP \left (v , n , \cos \left (x \right )\right )+c_{2} \LegendreQ \left (v , n , \cos \left (x \right )\right )\right ) \left (\sin ^{-n}\left (x \right )\right )\}\]