1.6.7 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 : Tuesday, September 30, 2025 at 03:48:25 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*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 16

ode:=diff(x(t),t) = 4*x(t)*(7-x(t)); 
ic:=[x(0) = 11]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 23

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

\begin{align*} x(t)&\to \frac {77 e^{28 t}}{11 e^{28 t}-4} \end{align*}

✓ Sympy. Time used: 0.244 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq((4*x(t) - 28)*x(t) + Derivative(x(t), t),0) 
ics = {x(0): 11} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {7}{1 - \frac {4 e^{- 28 t}}{11}} \]