\[ y''(x)=-(v-n) (n+v+1) y(x)-(2 n+1) \cot (x) y'(x) \] ✓ Mathematica : cpu = 0.2122 (sec), leaf count = 35
\[\left \{\left \{y(x)\to \left (-\sin ^2(x)\right )^{-n/2} \left (c_1 P_v^n(\cos (x))+c_2 Q_v^n(\cos (x))\right )\right \}\right \}\]
✓ Maple : cpu = 0.227 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) = \left ( \sin \left ( x \right ) \right ) ^{-n} \left ( {\it LegendreP} \left ( v,n,\cos \left ( x \right ) \right ) {\it \_C1}+{\it LegendreQ} \left ( v,n,\cos \left ( x \right ) \right ) {\it \_C2} \right ) \right \} \]