Internal problem ID [9062]
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')`]
\[ \boxed {y^{\prime }-\frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}=0} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) &= -2 x -2 \\ y \left (x \right ) &= \frac {\operatorname {LambertW}\left (\left (\ln \left (x +1\right )-c_{1} \right ) {\mathrm e}^{-2 x}\right )}{\ln \left (x +1\right )-c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.295 (sec). Leaf size: 29
DSolve[y'[x] == (y[x]*(2 + 2*x + y[x]))/((1 + x)*(-1 + 2*x + Log[y[x]])),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {W\left (e^{-2 x} (\log (x+1)+c_1)\right )}{\log (x+1)+c_1} \]