Internal problem ID [9093]
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')`]
\[ \boxed {y^{\prime }-\frac {\left (2 x +2+y x^{3}\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (1+x \right )}=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-\frac {\left (-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )+6 c_{1} -6 x \right ) {\mathrm e}^{-2 x}}{6}\right )-2 x} \]
✓ Solution by Mathematica
Time used: 60.52 (sec). Leaf size: 459
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 W\left (-\frac {1}{6} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1} y(x)\to \frac {6 W\left (\frac {1}{6} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1} y(x)\to \frac {6 W\left (-\frac {1}{6} \sqrt [3]{-1} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1} y(x)\to \frac {6 W\left (\frac {1}{6} \sqrt [3]{-1} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1} y(x)\to \frac {6 W\left (-\frac {1}{6} (-1)^{2/3} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1} y(x)\to \frac {6 W\left (\frac {1}{6} (-1)^{2/3} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1} \end{align*}