4.3.9 \(y'(x)=\cos ^2(x) \cos (y(x))\)

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

\[ \left \{ {\frac {\sin \left (2\,x \right ) }{4}}+{\frac {x}{2}}-\ln \left (\sec \left (y \relax (x ) \right ) +\tan \left (y \relax (x ) \right ) \right ) +{\it \_C1}=0 \right \} \] 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