Internal problem ID [8307]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 727.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [x=_G(y,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (2 x +2+y\right ) y}{\left (\ln \relax (y)+2 x -1\right ) \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 37
dsolve(diff(y(x),x) = (2*x+2+y(x))/(ln(y(x))+2*x-1)*y(x)/(x+1),y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = -2 x -2 \\ y \relax (x ) = {\mathrm e}^{-\LambertW \left (\left (\ln \left (x +1\right )-c_{1}\right ) {\mathrm e}^{-2 x}\right )-2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 124.635 (sec). Leaf size: 34
DSolve[y'[x] == (y[x]*(2 + 2*x + y[x]))/((1 + x)*(-1 + 2*x + Log[y[x]])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\text {ProductLog}\left (e^{-2 x} (\log (x+1)+c_1)\right )}{\log (x+1)+c_1} \\ y(x)\to 0 \\ \end{align*}