7.6.8 problem 8

Internal problem ID [178]
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 : 8
Date solved : Friday, February 07, 2025 at 08:01:22 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=7 x \left (x-13\right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=17 \end{align*}

✓ Solution by Maple

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

dsolve([diff(x(t),t)=7*x(t)*(x(t)-13),x(0) = 17],x(t), singsol=all)
 

\[ x = -\frac {221}{4 \,{\mathrm e}^{91 t}-17} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 18

DSolve[{D[x[t],t]==7*x[t]*(x[t]-13),{x[0]==17}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {221}{17-4 e^{91 t}} \]