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 : Tuesday, March 04, 2025 at 10:56:50 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*}

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

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

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

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

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

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

✓ Sympy. Time used: 0.359 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq((91 - 7*x(t))*x(t) + Derivative(x(t), t),0) 
ics = {x(0): 17} 
dsolve(ode,func=x(t),ics=ics)
 

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