23.1.222 problem 218

Internal problem ID [4829]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 218
Date solved : Tuesday, September 30, 2025 at 08:43:22 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 8

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

\[ y = {\mathrm e}^{c_1 x} \]

✓ Mathematica. Time used: 0.103 (sec). Leaf size: 18

ode=x*D[y[x],x]==y[x]*Log[y[x]]; 
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: 0.152 (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)
 

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