14.29.11 problem 11

Internal problem ID [2809]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 4. Qualitative theory of differential equations. Section 4.2 (Stability of linear systems). Page 383
Problem number : 11
Date solved : Monday, January 27, 2025 at 06:14:06 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

\[ x \left (t \right ) = \frac {1}{1+{\mathrm e}^{-t} c_1} \]

✓ Solution by Mathematica

Time used: 0.309 (sec). Leaf size: 29

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

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