ODE
\[ y'(x)=\cos ^2(x) \cos (y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.348097 (sec), leaf count = 23
\[\left \{\left \{y(x)\to 2 \tan ^{-1}\left (\tanh \left (\frac {1}{8} (2 x+\sin (2 x)+c_1)\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.139 (sec), leaf count = 69
\[\left [y \left (x \right ) = \arctan \left (\frac {\textit {\_C1}^{2} {\mathrm e}^{x +\frac {\sin \left (2 x \right )}{2}}-1}{\textit {\_C1}^{2} {\mathrm e}^{x +\frac {\sin \left (2 x \right )}{2}}+1}, \frac {2 \textit {\_C1} \,{\mathrm e}^{\frac {x}{2}+\frac {\sin \left (2 x \right )}{4}}}{\textit {\_C1}^{2} {\mathrm e}^{x +\frac {\sin \left (2 x \right )}{2}}+1}\right )\right ]\] 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))
Maple raw output
[y(x) = arctan((_C1^2*exp(x+1/2*sin(2*x))-1)/(_C1^2*exp(x+1/2*sin(2*x))+1),2*_C1/(_C1^2*exp(x+1/2*sin(2*x))+1)*exp(1/2*x+1/4*sin(2*x)))]