4.3.16 $y^{\prime }(x)+\tan (x)\sec (x){\cos }^2(y(x))=0$

ODE
$$y^{\prime }(x)+\tan (x)\sec (x){\cos }^2(y(x))=0$$ 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

$$\{\frac{\mathit{\_}\mathit{C}\mathit{1}\cos (x-y\left(x\right))+\mathit{\_}\mathit{C}\mathit{1}\cos (x+y\left(x\right))+\sin (x+y\left(x\right))-\sin (x-y\left(x\right))+2\cos \left(y\left(x\right)\right)}{\cos (x-y\left(x\right))+\cos (x+y\left(x\right))}=0\}$$ 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