60.1.117 problem 118

Internal problem ID [10131]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 118
Date solved : Monday, January 27, 2025 at 06:29:14 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }-y \ln \left (y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 8

dsolve(x*diff(y(x),x) - y(x)*ln(y(x))=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{c_{1} x} \]

✓ Solution by Mathematica

Time used: 0.186 (sec). Leaf size: 18

DSolve[x*D[y[x],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*}