\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \cot \left ( x \right ) +v \left ( v+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 0.141 (sec), leaf count = 45 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_2$F$_1$}(-{\frac {v}{2}},{\frac {1}{2}}+{\frac {v}{2}};\,{\frac {1}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})} +{\it \_C2}\,\cos \left ( x \right ) {\mbox {$_2$F$_1$}(1+{\frac {v}{2}},{\frac {1}{2}}-{\frac {v}{2}};\,{\frac {3}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})} \right \} \]