44.1.21 problem 23

Internal problem ID [6896]
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. Exercises 1.1 at page 12
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:34:20 PM
CAS classification : [_quadrature]

\begin{align*} p^{\prime }&=p \left (1-p\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(p(t),t)=p(t)*(1-p(t)),p(t), singsol=all)
 

\[ p = \frac {1}{1+{\mathrm e}^{-t} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.322 (sec). Leaf size: 29

DSolve[D[p[t],t]==p[t]*(1-p[t]),p[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} p(t)\to \frac {e^t}{e^t+e^{c_1}} \\ p(t)\to 0 \\ p(t)\to 1 \\ \end{align*}