ODE
\[ y'(x)=\cos ^2(x) \cos (y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.050805 (sec), leaf count = 23
\[\left \{\left \{y(x)\to 2 \tan ^{-1}\left (\tanh \left (\frac {1}{8} \left (c_1+2 x+\sin (2 x)\right )\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 24
\[ \left \{ {\frac {\sin \left ( 2\,x \right ) }{4}}+{\frac {x}{2}}-\ln \left ( \sec \left ( y \left ( x \right ) \right ) +\tan \left ( y \left ( x \right ) \right ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y'[x] == Cos[x]^2*Cos[y[x]],y[x],x]
Mathematica raw output
{{y[x] -> 2*ArcTan[Tanh[(2*x + C[1] + Sin[2*x])/8]]}}
Maple raw input
dsolve(diff(y(x),x) = cos(x)^2*cos(y(x)), y(x),'implicit')
Maple raw output
1/4*sin(2*x)+1/2*x-ln(sec(y(x))+tan(y(x)))+_C1 = 0