7.6.1 problem 1

Internal problem ID [171]
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 : 1
Date solved : Tuesday, March 04, 2025 at 10:56:17 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=x-x^{2} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=2 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 14

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

\[ x = -\frac {2}{{\mathrm e}^{-t}-2} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 19

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

\[ x(t)\to \frac {2 e^t}{2 e^t-1} \]

✓ Sympy. Time used: 0.355 (sec). Leaf size: 12

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

\[ x{\left (t \right )} = \frac {1}{1 - \frac {e^{- t}}{2}} \]