44.3.8 problem 14

Internal problem ID [6989]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 14
Date solved : Monday, January 27, 2025 at 02:39:58 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \left (y-3\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x)=y(x)*(y(x)-3),y(x), singsol=all)
 

\[ y = \frac {3}{1+3 \,{\mathrm e}^{3 x} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.168 (sec). Leaf size: 29

DSolve[D[y[x],x]==y[x]*(y[x]-3),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {3}{1+e^{3 (x+c_1)}} \\ y(x)\to 0 \\ y(x)\to 3 \\ \end{align*}