44.1.19 problem 21

Internal problem ID [6894]
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 : 21
Date solved : Monday, January 27, 2025 at 02:34:16 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 19

dsolve(diff(x(t),t)=(x(t)-1)*(1-2*x(t)),x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {-1+c_{1} {\mathrm e}^{t}}{c_{1} {\mathrm e}^{t}-2} \]

✓ Solution by Mathematica

Time used: 0.785 (sec). Leaf size: 40

DSolve[D[x[t],t]==(x[t]-1)*(1-2*x[t]),x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {e^t-e^{c_1}}{e^t-2 e^{c_1}} \\ x(t)\to \frac {1}{2} \\ x(t)\to 1 \\ \end{align*}