Internal problem ID [7658]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 77.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\cos \left (a y+x b \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 65
dsolve(diff(y(x),x) - cos(a*y(x)+b*x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {b x +2 \arctan \left (\frac {\tanh \left (\frac {c_{1} \sqrt {\left (a +b \right ) \left (a -b \right )}}{2}-\frac {x \sqrt {\left (a +b \right ) \left (a -b \right )}}{2}\right ) \sqrt {\left (a +b \right ) \left (a -b \right )}}{a -b}\right )}{a} \]
✓ Solution by Mathematica
Time used: 60.399 (sec). Leaf size: 58
DSolve[y'[x] - Cos[a*y[x]+b*x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-b x+2 \text {ArcTan}\left (\frac {(a+b) \tanh \left (\frac {1}{2} \sqrt {(a-b) (a+b)} (x-c_1)\right )}{\sqrt {(a-b) (a+b)}}\right )}{a} \\ \end{align*}