65.2.4 problem 7.1 (iv)

Internal problem ID [13717]
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 (iv)
Date solved : Tuesday, January 28, 2025 at 05:56:00 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=-x \left (-x+1\right ) \left (2-x\right ) \end{align*}

✓ Solution by Maple

Time used: 0.155 (sec). Leaf size: 34

dsolve(diff(x(t),t)=-x(t)*(1-x(t))*(2-x(t)),x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 53

DSolve[D[x[t],t]==-x[t]*(1-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]-1) K[1]}dK[1]\&\right ][-t+c_1] \\ x(t)\to 0 \\ x(t)\to 1 \\ x(t)\to 2 \\ \end{align*}