Internal problem ID [12878]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.2. page
33
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y \left (-y+1\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(t),t)=y(t)*(1-y(t)),y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{1+{\mathrm e}^{-t} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.394 (sec). Leaf size: 29
DSolve[y'[t]==y[t]*(1-y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^t}{e^t+e^{c_1}} \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}