4.3.29 \(y'(x)+\csc (2 x) \sin (2 y(x))=0\)

ODE
\[ y'(x)+\csc (2 x) \sin (2 y(x))=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.183718 (sec), leaf count = 15

\[\left \{\left \{y(x)\to \cot ^{-1}\left (e^{-2 c_1} \tan (x)\right )\right \}\right \}\]

Maple
cpu = 0.023 (sec), leaf count = 31

\[ \left \{ \ln \left (\csc \left (2\,x \right ) -\cot \left (2\,x \right ) \right ) +\ln \left (\csc \left (2\,y \relax (x ) \right ) -\cot \left (2\,y \relax (x ) \right ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[Csc[2*x]*Sin[2*y[x]] + y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> ArcCot[Tan[x]/E^(2*C[1])]}}

Maple raw input

dsolve(diff(y(x),x)+csc(2*x)*sin(2*y(x)) = 0, y(x),'implicit')

Maple raw output

ln(csc(2*x)-cot(2*x))+ln(csc(2*y(x))-cot(2*y(x)))+_C1 = 0