7.6.1 problem 1

Internal problem ID [171]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.7 (population models). Problems at page 82
Problem number : 1
Date solved : Friday, February 07, 2025 at 08:00:41 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=x-x^{2} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 14

dsolve([diff(x(t),t)=x(t)-x(t)^2,x(0) = 2],x(t), singsol=all)
 

\[ x = -\frac {2}{{\mathrm e}^{-t}-2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 19

DSolve[{D[x[t],t]==x[t]-x[t]^2,{x[0]==2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {2 e^t}{2 e^t-1} \]