29.8.10 problem 215

Internal problem ID [4815]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 215
Date solved : Tuesday, March 04, 2025 at 07:19:46 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 8

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

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

✓ Mathematica. Time used: 0.169 (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: 0.270 (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)
 

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