Internal problem ID [6143]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y \ln \left (y\right )-y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 8
dsolve(y(x)*ln(y(x))-x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{c_{1} x} \]
✓ Solution by Mathematica
Time used: 0.172 (sec). Leaf size: 18
DSolve[y[x]*Log[y[x]]-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{e^{c_1} x} y(x)\to 1 \end{align*}