Internal problem ID [7698]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 118.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{\prime }-y \ln \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 8
dsolve(x*diff(y(x),x) - y(x)*ln(y(x))=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{c_{1} x} \]
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 18
DSolve[x*y'[x] - y[x]*Log[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{e^{c_1} x} \\ y(x)\to 1 \\ \end{align*}