ODE
\[ y'(x)=\cot (x) \cot (y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.307986 (sec), leaf count = 29
\[\left \{\left \{y(x)\to -\cos ^{-1}\left (-\frac {1}{2} c_1 \csc (x)\right )\right \},\left \{y(x)\to \cos ^{-1}\left (-\frac {1}{2} c_1 \csc (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 13
\[\left [y \left (x \right ) = \arccos \left (\frac {1}{\sin \left (x \right ) \textit {\_C1}}\right )\right ]\] Mathematica raw input
DSolve[y'[x] == Cot[x]*Cot[y[x]],y[x],x]
Mathematica raw output
{{y[x] -> -ArcCos[-1/2*(C[1]*Csc[x])]}, {y[x] -> ArcCos[-1/2*(C[1]*Csc[x])]}}
Maple raw input
dsolve(diff(y(x),x) = cot(x)*cot(y(x)), y(x))
Maple raw output
[y(x) = arccos(1/sin(x)/_C1)]