4.3.21 \(y'(x)+\tan (x) \cot (y(x))=0\)

ODE
\[ y'(x)+\tan (x) \cot (y(x))=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0450254 (sec), leaf count = 29

\[\left \{\left \{y(x)\to -\cos ^{-1}\left (\frac {1}{2} c_1 \sec (x)\right )\right \},\left \{y(x)\to \cos ^{-1}\left (\frac {1}{2} c_1 \sec (x)\right )\right \}\right \}\]

Maple
cpu = 0.005 (sec), leaf count = 12

\[ \left \{ {\it \_C1}+\ln \left (\cos \relax (x ) \right ) +\ln \left (\cos \left (y \relax (x ) \right ) \right ) =0 \right \} \] Mathematica raw input

DSolve[Cot[y[x]]*Tan[x] + y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -ArcCos[(C[1]*Sec[x])/2]}, {y[x] -> ArcCos[(C[1]*Sec[x])/2]}}

Maple raw input

dsolve(diff(y(x),x)+tan(x)*cot(y(x)) = 0, y(x),'implicit')

Maple raw output

_C1+ln(cos(x))+ln(cos(y(x))) = 0