Internal problem ID [7697]
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]
\[ \boxed {y^{\prime } x -y \ln \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 8
dsolve(x*diff(y(x),x) - y(x)*ln(y(x))=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x c_{1}} \]
✓ Solution by Mathematica
Time used: 0.172 (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*}