4.3.20 \(y'(x)=\tan (x) \cot (y(x))\)

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0635995 (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 = 0.005 (sec), leaf count = 14

\[ \left \{ -\ln \left (\cos \relax (x ) \right ) +\ln \left (\cos \left (y \relax (x ) \right ) \right ) +{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

-ln(cos(x))+ln(cos(y(x)))+_C1 = 0