77.1.68 problem 88 (page 123)

Internal problem ID [17887]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 88 (page 123)
Date solved : Monday, March 31, 2025 at 04:48:09 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.16 (sec). Leaf size: 18

ode=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^{x+c_1}} \\ y(x)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.234 (sec). Leaf size: 8

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

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