ODE
\[ y'(x)=a+b \cos (y(x)) \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Independent variable missing
Mathematica ✓
cpu = 0.297486 (sec), leaf count = 47
\[\left \{\left \{y(x)\to 2 \tan ^{-1}\left (\frac {(a+b) \tanh \left (\frac {1}{2} \sqrt {b^2-a^2} (x+c_1)\right )}{\sqrt {b^2-a^2}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.043 (sec), leaf count = 56
\[\left [y \left (x \right ) = 2 \arctan \left (\frac {\tan \left (\frac {\textit {\_C1} \sqrt {\left (a +b \right ) \left (a -b \right )}}{2}+\frac {x \sqrt {\left (a +b \right ) \left (a -b \right )}}{2}\right ) \sqrt {\left (a +b \right ) \left (a -b \right )}}{a -b}\right )\right ]\] Mathematica raw input
DSolve[y'[x] == a + b*Cos[y[x]],y[x],x]
Mathematica raw output
{{y[x] -> 2*ArcTan[((a + b)*Tanh[(Sqrt[-a^2 + b^2]*(x + C[1]))/2])/Sqrt[-a^2 + b^2]]}}
Maple raw input
dsolve(diff(y(x),x) = a+b*cos(y(x)), y(x))
Maple raw output
[y(x) = 2*arctan(tan(1/2*_C1*((a+b)*(a-b))^(1/2)+1/2*x*((a+b)*(a-b))^(1/2))*((a+b)*(a-b))^(1/2)/(a-b))]