7.6.7 problem 7

Internal problem ID [177]
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 : 7
Date solved : Friday, February 07, 2025 at 08:01:15 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=4 x \left (7-x\right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=11 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 16

dsolve([diff(x(t),t)=4*x(t)*(7-x(t)),x(0) = 11],x(t), singsol=all)
 

\[ x = -\frac {77}{4 \,{\mathrm e}^{-28 t}-11} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 23

DSolve[{D[x[t],t]==4*x[t]*(7-x[t]),{x[0]==11}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {77 e^{28 t}}{11 e^{28 t}-4} \]