Internal problem ID [2858]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 109.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-a -b \cos \left (A x +B y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 96
dsolve(diff(y(x),x) = a+b*cos(A*x+B*y(x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {A x +2 \arctan \left (\frac {\tan \left (\frac {c_{1} \sqrt {\left (a B +b B +A \right ) \left (a B -b B +A \right )}}{2}-\frac {x \sqrt {\left (a B +b B +A \right ) \left (a B -b B +A \right )}}{2}\right ) \sqrt {\left (a B +b B +A \right ) \left (a B -b B +A \right )}}{a B -b B +A}\right )}{B} \]
✓ Solution by Mathematica
Time used: 60.405 (sec). Leaf size: 80
DSolve[y'[x]==a+b Cos[A x+ B y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {A x+2 \text {ArcTan}\left (\frac {(B (a+b)+A) \tanh \left (\frac {1}{2} (-x+c_1) \sqrt {-((B (a-b)+A) (B (a+b)+A))}\right )}{\sqrt {-((B (a-b)+A) (B (a+b)+A))}}\right )}{B} \\ \end{align*}