ODE
\[ y'(x)=\tan (x) \cot (y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.271847 (sec), leaf count = 29
\[\left \{\left \{y(x)\to -\cos ^{-1}\left (\frac {1}{2} c_1 \cos (x)\right )\right \},\left \{y(x)\to \cos ^{-1}\left (\frac {1}{2} c_1 \cos (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.057 (sec), leaf count = 11
\[\left [y \left (x \right ) = \arccos \left (\frac {\cos \left (x \right )}{\textit {\_C1}}\right )\right ]\] Mathematica raw input
DSolve[y'[x] == Cot[y[x]]*Tan[x],y[x],x]
Mathematica raw output
{{y[x] -> -ArcCos[(C[1]*Cos[x])/2]}, {y[x] -> ArcCos[(C[1]*Cos[x])/2]}}
Maple raw input
dsolve(diff(y(x),x) = tan(x)*cot(y(x)), y(x))
Maple raw output
[y(x) = arccos(cos(x)/_C1)]