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