90.1.4 problem 15

Internal problem ID [25028]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 15
Date solved : Thursday, October 02, 2025 at 11:47:33 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 y \left (-1+y\right ) \end{align*}

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

ode:=diff(y(t),t) = 2*y(t)*(y(t)-1); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {1}{1+{\mathrm e}^{2 t} c_1} \]

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 27

ode=D[y[t],{t,1}]==2*y[t]*(y[t]-1); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{1+e^{2 t+c_1}}\\ y(t)&\to 0\\ y(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.203 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*(y(t) - 1)*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{C_{1} - e^{2 t}} \]