Internal problem ID [8338]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 758.
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+x^{3} y\right ) y}{\left (\ln \relax (y)+2 x -1\right ) \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 41
dsolve(diff(y(x),x) = (2*x+2+x^3*y(x))/(ln(y(x))+2*x-1)*y(x)/(x+1),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-\frac {\left (-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )+6 c_{1}-6 x \right ) {\mathrm e}^{-2 x}}{6}\right )-2 x} \]
✓ Solution by Mathematica
Time used: 0.947 (sec). Leaf size: 435
DSolve[y'[x] == (y[x]*(2 + 2*x + x^3*y[x]))/((1 + x)*(-1 + 2*x + Log[y[x]])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {6 \text {ProductLog}\left (-\frac {1}{6} \sqrt [6]{e^{-12 x} (x (x (2 x-3)+6)-6 \log (x+1)+6 c_1){}^6}\right )}{x (x (2 x-3)+6)-6 \log (x+1)+6 c_1} \\ y(x)\to \frac {6 \text {ProductLog}\left (\frac {1}{6} \sqrt [6]{e^{-12 x} (x (x (2 x-3)+6)-6 \log (x+1)+6 c_1){}^6}\right )}{x (x (2 x-3)+6)-6 \log (x+1)+6 c_1} \\ y(x)\to \frac {6 \text {ProductLog}\left (-\frac {1}{6} \sqrt [3]{-1} \sqrt [6]{e^{-12 x} (x (x (2 x-3)+6)-6 \log (x+1)+6 c_1){}^6}\right )}{x (x (2 x-3)+6)-6 \log (x+1)+6 c_1} \\ y(x)\to \frac {6 \text {ProductLog}\left (\frac {1}{6} \sqrt [3]{-1} \sqrt [6]{e^{-12 x} (x (x (2 x-3)+6)-6 \log (x+1)+6 c_1){}^6}\right )}{x (x (2 x-3)+6)-6 \log (x+1)+6 c_1} \\ y(x)\to \frac {6 \text {ProductLog}\left (-\frac {1}{6} (-1)^{2/3} \sqrt [6]{e^{-12 x} (x (x (2 x-3)+6)-6 \log (x+1)+6 c_1){}^6}\right )}{x (x (2 x-3)+6)-6 \log (x+1)+6 c_1} \\ y(x)\to \frac {6 \text {ProductLog}\left (\frac {1}{6} (-1)^{2/3} \sqrt [6]{e^{-12 x} (x (x (2 x-3)+6)-6 \log (x+1)+6 c_1){}^6}\right )}{x (x (2 x-3)+6)-6 \log (x+1)+6 c_1} \\ \end{align*}