38.5.29 problem 29

Internal problem ID [8377]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 29
Date solved : Tuesday, September 30, 2025 at 05:33:05 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&={\mathrm e} \\ \end{align*}

✓ Maple. Time used: 0.088 (sec). Leaf size: 9

ode:=diff(y(x),x) = -y(x)*ln(y(x)); 
ic:=[y(0) = exp(1)]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 12

ode=D[y[x],x]==-y[x]*Log[y[x]]; 
ic={y[0]==Exp[1]}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{e^{-x}} \end{align*}

✓ Sympy. Time used: 0.154 (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 = {y(0): E} 
dsolve(ode,func=y(x),ics=ics)
 

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