Internal problem ID [10631]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-x \left (2-x\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(x(t),t)=x(t)*(2-x(t)),x(t), singsol=all)
\[ x \left (t \right ) = \frac {2}{1+2 \,{\mathrm e}^{-2 t} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.32 (sec). Leaf size: 24
DSolve[x'[t]==x[t]*(2-x[t]),x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 1+\tanh (t-c_1) \\ x(t)\to 0 \\ x(t)\to 2 \\ \end{align*}