Internal problem ID [2860]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 111.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-a -b \cos \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 56
dsolve(diff(y(x),x) = a+b*cos(y(x)),y(x), singsol=all)
\[ y \relax (x ) = 2 \arctan \left (\frac {\tan \left (\frac {c_{1} \sqrt {\left (a +b \right ) \left (a -b \right )}}{2}+\frac {x \sqrt {\left (a +b \right ) \left (a -b \right )}}{2}\right ) \sqrt {\left (a +b \right ) \left (a -b \right )}}{a -b}\right ) \]
✓ Solution by Mathematica
Time used: 60.125 (sec). Leaf size: 47
DSolve[y'[x]==a+b Cos[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \text {ArcTan}\left (\frac {(a+b) \tanh \left (\frac {1}{2} \sqrt {b^2-a^2} (x+c_1)\right )}{\sqrt {b^2-a^2}}\right ) \\ \end{align*}