4.3.18 \(y'(x)+\cot (x) \cot (y(x))=0\)

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0608963 (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 = 0.006 (sec), leaf count = 14

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

ln(sin(x))-ln(cos(y(x)))+_C1 = 0