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 = 1.32752 (sec), leaf count = 13
\[\left \{\left \{y(x)\to \tan ^{-1}(-\sec (x)+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 18
\[\left [y \left (x \right ) = -\arctan \left (\frac {\textit {\_C1} \cos \left (x \right )+1}{\cos \left (x \right )}\right )\right ]\] Mathematica raw input
DSolve[Cos[y[x]]^2*Sec[x]*Tan[x] + y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ArcTan[C[1] - Sec[x]]}}
Maple raw input
dsolve(diff(y(x),x)+tan(x)*sec(x)*cos(y(x))^2 = 0, y(x))
Maple raw output
[y(x) = -arctan((_C1*cos(x)+1)/cos(x))]