65.2.2 problem 7.1 (ii)

Internal problem ID [13715]
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 : Tuesday, January 28, 2025 at 05:55:52 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[x[t],t]==x[t]*(2-x[t]),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*}