\[ y''(x)=\cot (2 x) y'(x)-2 y(x) \] ✓ Mathematica : cpu = 0.186659 (sec), leaf count = 80
\[\left \{\left \{y(x)\to c_1 \left (\cos ^2(x)-\frac {1}{2}\right )-\frac {2}{3} c_2 \cos ^{\frac {3}{2}}(x) \left (2 \cos ^2(x) \, _2F_1\left (\frac {1}{4},\frac {3}{4};\frac {7}{4};\cos ^2(x)\right )-\, _2F_1\left (\frac {1}{4},\frac {3}{4};\frac {7}{4};\cos ^2(x)\right )+3 \left (1-\cos ^2(x)\right )^{3/4}\right )\right \}\right \}\]
✓ Maple : cpu = 0.405 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( \sin \left ( 2\,x \right ) \right ) ^{{\frac {3}{4}}}{\it LegendreP} \left ( {\frac {1}{4}},{\frac {3}{4}},\cos \left ( 2\,x \right ) \right ) +{\it \_C2}\, \left ( \sin \left ( 2\,x \right ) \right ) ^{{\frac {3}{4}}}{\it LegendreQ} \left ( {\frac {1}{4}},{\frac {3}{4}},\cos \left ( 2\,x \right ) \right ) \right \} \]