\[ v (v+1) y(x)+y''(x)+\cot (x) y'(x)=0 \] ✓ Mathematica : cpu = 0.129742 (sec), leaf count = 20
\[\{\{y(x)\to c_1 P_v(\cos (x))+c_2 Q_v(\cos (x))\}\}\] ✓ Maple : cpu = 0.288 (sec), leaf count = 45
\[\left \{y \left (x \right ) = c_{2} \hypergeom \left (\left [\frac {v}{2}+1, -\frac {v}{2}+\frac {1}{2}\right ], \left [\frac {3}{2}\right ], \cos ^{2}\left (x \right )\right ) \cos \left (x \right )+c_{1} \hypergeom \left (\left [-\frac {v}{2}, \frac {v}{2}+\frac {1}{2}\right ], \left [\frac {1}{2}\right ], \cos ^{2}\left (x \right )\right )\right \}\]