ODE
\[ y'(x)+\cot (x) \cot (y(x))=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.279734 (sec), leaf count = 29
\[\left \{\left \{y(x)\to -\cos ^{-1}\left (-\frac {1}{2} c_1 \sin (x)\right )\right \},\left \{y(x)\to \cos ^{-1}\left (-\frac {1}{2} c_1 \sin (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.053 (sec), leaf count = 9
\[[y \left (x \right ) = \arccos \left (\sin \left (x \right ) \textit {\_C1} \right )]\] Mathematica raw input
DSolve[Cot[x]*Cot[y[x]] + y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -ArcCos[-1/2*(C[1]*Sin[x])]}, {y[x] -> ArcCos[-1/2*(C[1]*Sin[x])]}}
Maple raw input
dsolve(diff(y(x),x)+cot(x)*cot(y(x)) = 0, y(x))
Maple raw output
[y(x) = arccos(sin(x)*_C1)]