7.6.2 problem 2

Internal problem ID [172]
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 : 2
Date solved : Friday, February 07, 2025 at 08:00:48 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=10 x-x^{2} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 16

dsolve([diff(x(t),t)=10*x(t)-x(t)^2,x(0) = 1],x(t), singsol=all)
 

\[ x = \frac {10}{1+9 \,{\mathrm e}^{-10 t}} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 21

DSolve[{D[x[t],t]==10*x[t]-x[t]^2,{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {10 e^{10 t}}{e^{10 t}+9} \]