Internal problem ID [11661]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }+x \left (1-x\right ) \left (-x+2\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(diff(x(t),t)=-x(t)*(1-x(t))*(2-x(t)),x(t), singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{t} c_{1}}{\sqrt {-1+{\mathrm e}^{2 t} c_{1}^{2}}}+1 \]
✓ Solution by Mathematica
Time used: 19.885 (sec). Leaf size: 159
DSolve[x'[t]==-x[t]*(1-x[t])*(2-x[t]),x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {e^{2 t}-\sqrt {e^{4 t}+e^{2 (t+c_1)}}+e^{2 c_1}}{e^{2 t}+e^{2 c_1}} x(t)\to \frac {e^{2 t}+\sqrt {e^{4 t}+e^{2 (t+c_1)}}+e^{2 c_1}}{e^{2 t}+e^{2 c_1}} x(t)\to 0 x(t)\to 1 x(t)\to 2 x(t)\to 1-e^{-2 t} \sqrt {e^{4 t}} x(t)\to e^{-2 t} \sqrt {e^{4 t}}+1 \end{align*}