44.5.29 problem 29

Internal problem ID [7091]
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, January 28, 2025 at 08:48:44 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*}

✓ Solution by Maple

Time used: 0.067 (sec). Leaf size: 9

dsolve([diff(y(x),x)=-y(x)*ln(y(x)),y(0) = exp(1)],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 12

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

\[ y(x)\to e^{e^{-x}} \]