\[ y(x)^2 \log (y(x)) \left (\cos ^2(x)-n^2 \cot ^2(x)\right )+y(x) y''(x)-y'(x)^2+y(x) y'(x) (\tan (x)+\cot (x))=0 \] ✗ Mathematica : cpu = 300.004 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.57 (sec), leaf count = 81
\[ \left \{ y \left ( x \right ) ={1{{\rm e}^{{\frac {{{\sl J}_{n}\left (\sin \left ( x \right ) \right )}{\it \_C1}}{\sin \left ( x \right ) \left ( {{\sl J}_{n+1}\left (\sin \left ( x \right ) \right )}{{\sl Y}_{n}\left (\sin \left ( x \right ) \right )}-{{\sl Y}_{n+1}\left (\sin \left ( x \right ) \right )}{{\sl J}_{n}\left (\sin \left ( x \right ) \right )} \right ) }}}} \left ( {{\rm e}^{{\frac {{{\sl Y}_{n}\left (\sin \left ( x \right ) \right )}{\it \_C2}}{\sin \left ( x \right ) \left ( {{\sl J}_{n+1}\left (\sin \left ( x \right ) \right )}{{\sl Y}_{n}\left (\sin \left ( x \right ) \right )}-{{\sl Y}_{n+1}\left (\sin \left ( x \right ) \right )}{{\sl J}_{n}\left (\sin \left ( x \right ) \right )} \right ) }}}} \right ) ^{-1}} \right \} \]