Internal problem ID [7699]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 119.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {x y^{\prime }-y \left (\ln \left (y x \right )-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 14
dsolve(x*diff(y(x),x) - y(x)*(ln(x*y(x))-1)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{\frac {x}{c_{1}}}}{x} \]
✓ Solution by Mathematica
Time used: 0.32 (sec). Leaf size: 24
DSolve[x*y'[x] - y[x]*(Log[x*y[x]]-1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{e^{c_1} x}}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}