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 : Wednesday, March 05, 2025 at 05:06:43 AM
CAS classification : [_separable]

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

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

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

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

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

ode=y[x]*Log[y[x]]-x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.269 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + y(x)*log(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{C_{1} x} \]