Internal problem ID [8352]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 772.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [x=_G(y,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (x +1+\ln \relax (y) x \right ) \ln \relax (y) y}{x \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x) = (x+1+ln(y(x))*x)*ln(y(x))*y(x)/x/(x+1),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {x}{\ln \left (x +1\right )+c_{1}-x}} \]
✓ Solution by Mathematica
Time used: 0.394 (sec). Leaf size: 26
DSolve[y'[x] == (Log[y[x]]*(1 + x + x*Log[y[x]])*y[x])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {x}{-x+\log (x+1)+c_1}} \\ y(x)\to 1 \\ \end{align*}