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 : Saturday, March 29, 2025 at 04:38:09 PM
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*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.397 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(x(t)**2 - 10*x(t) + Derivative(x(t), t),0) 
ics = {x(0): 1} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {10}{1 + 9 e^{- 10 t}} \]