50.2.5 problem 1(e)

Internal problem ID [7811]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:23:47 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 18

DSolve[y[x]*Log[y[x]]-x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{e^{c_1} x} \\ y(x)\to 1 \\ \end{align*}