72.1.14 problem 17

Internal problem ID [14614]
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
Date solved : Tuesday, January 28, 2025 at 06:44:36 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

\[ y = \frac {1}{1+{\mathrm e}^{-t} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.231 (sec). Leaf size: 42

DSolve[D[y[t],t]==y[t]*(1-y[t]),y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]}dK[1]\&\right ][-t+c_1] \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}