Internal problem ID [8386]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 806.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-\sin \left (2 y\right ) x -\sin \left (2 y\right )+x \cos \left (2 y\right )+x}{2 x \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 22
dsolve(diff(y(x),x) = 1/2*(-sin(2*y(x))*x-sin(2*y(x))+x*cos(2*y(x))+x)/x/(x+1),y(x), singsol=all)
\[ y \relax (x ) = -\arctan \left (\frac {\ln \left (x +1\right )-x -c_{1}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 7.17 (sec). Leaf size: 80
DSolve[y'[x] == (x/2 + (x*Cos[2*y[x]])/2 - Sin[2*y[x]]/2 - (x*Sin[2*y[x]])/2)/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcTan}\left (\frac {x-\log (x+1)-c_1}{x}\right ) \\ y(x)\to -\frac {1}{2} i \left (\log \left (-\frac {i}{x}\right )-\log \left (\frac {i}{x}\right )\right ) \\ y(x)\to \frac {1}{2} i \left (\log \left (-\frac {i}{x}\right )-\log \left (\frac {i}{x}\right )\right ) \\ \end{align*}