4.3.16 \(y'(x)+\tan (x) \sec (x) \cos ^2(y(x))=0\)

ODE
\[ y'(x)+\tan (x) \sec (x) \cos ^2(y(x))=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0 (sec), leaf count = 0 , $Failed

$Failed

Maple
cpu = 0.02 (sec), leaf count = 55

\[ \left \{ {\frac {{\it \_C1}\,\cos \left (x-y \relax (x ) \right ) +{\it \_C1}\,\cos \left (x+y \relax (x ) \right ) +\sin \left (x+y \relax (x ) \right ) -\sin \left (x-y \relax (x ) \right ) +2\,\cos \left (y \relax (x ) \right ) }{\cos \left (x-y \relax (x ) \right ) +\cos \left (x+y \relax (x ) \right ) }}=0 \right \} \] Mathematica raw input

DSolve[Cos[y[x]]^2*Sec[x]*Tan[x] + y'[x] == 0,y[x],x]

Mathematica raw output

{}

Maple raw input

dsolve(diff(y(x),x)+tan(x)*sec(x)*cos(y(x))^2 = 0, y(x),'implicit')

Maple raw output

(_C1*cos(x-y(x))+_C1*cos(x+y(x))+sin(x+y(x))-sin(x-y(x))+2*cos(y(x)))/(cos(x-y(x
))+cos(x+y(x))) = 0