72.1.14 problem 17

Internal problem ID [14535]
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 : Thursday, March 13, 2025 at 03:32:50 AM
CAS classification : [_quadrature]

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

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

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

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

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

ode=D[y[t],t]==y[t]*(1-y[t]); 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.348 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-(1 - y(t))*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {1}{C_{1} e^{- t} + 1} \]