65.2.2 problem 7.1 (ii)

Internal problem ID [13636]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 7, Scalar autonomous ODEs. Exercises page 56
Problem number : 7.1 (ii)
Date solved : Wednesday, March 05, 2025 at 10:05:46 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=x \left (2-x\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=diff(x(t),t) = x(t)*(2-x(t)); 
dsolve(ode,x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.215 (sec). Leaf size: 42

ode=D[x[t],t]==x[t]*(2-x[t]); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-2) K[1]}dK[1]\&\right ][-t+c_1] \\ x(t)\to 0 \\ x(t)\to 2 \\ \end{align*}

✓ Sympy. Time used: 0.352 (sec). Leaf size: 12

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

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