\[ v (v+1) y(x)+y''(x)+\cot (x) y'(x)=0 \] ✓ Mathematica : cpu = 0.112921 (sec), leaf count = 20
\[\{\{y(x)\to c_1 P_v(\cos (x))+c_2 Q_v(\cos (x))\}\}\] ✓ Maple : cpu = 0.196 (sec), leaf count = 45
\[y \relax (x ) = c_{1} \hypergeom \left (\left [-\frac {v}{2}, \frac {1}{2}+\frac {v}{2}\right ], \left [\frac {1}{2}\right ], \cos ^{2}\relax (x )\right )+c_{2} \cos \relax (x ) \hypergeom \left (\left [1+\frac {v}{2}, \frac {1}{2}-\frac {v}{2}\right ], \left [\frac {3}{2}\right ], \cos ^{2}\relax (x )\right )\]