Internal problem ID [8342]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 762.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {\left (\ln \relax (y) x +\ln \relax (y)-x \right ) y}{x \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 22
dsolve(diff(y(x),x) = -(ln(y(x))*x+ln(y(x))-x)*y(x)/x/(x+1),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e} \left (x +1\right )^{-\frac {1}{x}} {\mathrm e}^{\frac {c_{1}}{x}} \]
✓ Solution by Mathematica
Time used: 0.373 (sec). Leaf size: 26
DSolve[y'[x] == ((x - Log[y[x]] - x*Log[y[x]])*y[x])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+1)^{-1/x} e^{1-\frac {c_1}{x}} \\ \end{align*}