Internal problem ID [7657]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 76.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-a \cos \relax (y)+b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 54
dsolve(diff(y(x),x) - a*cos(y(x)) + b=0,y(x), singsol=all)
\[ y \relax (x ) = 2 \arctan \left (\frac {\tanh \left (\frac {c_{1} \sqrt {\left (a +b \right ) \left (a -b \right )}}{2}+\frac {x \sqrt {\left (a +b \right ) \left (a -b \right )}}{2}\right ) \sqrt {\left (a +b \right ) \left (a -b \right )}}{a +b}\right ) \]
✓ Solution by Mathematica
Time used: 60.211 (sec). Leaf size: 51
DSolve[y'[x] - a*Cos[y[x]] + b==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \text {ArcTan}\left (\frac {\sqrt {(a-b) (a+b)} \tanh \left (\frac {1}{2} \sqrt {(a-b) (a+b)} (x-c_1)\right )}{a+b}\right ) \\ \end{align*}