90.3.1 problem 1

Internal problem ID [25065]
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 41
Problem number : 1
Date solved : Thursday, October 02, 2025 at 11:48:10 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 y \left (5-y\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(y(t),t) = 2*y(t)*(5-y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {5}{1+5 \,{\mathrm e}^{-10 t} c_1} \]

✓ Mathematica. Time used: 0.178 (sec). Leaf size: 36

ode=D[y[t],{t,1}]==2*y[t]*(5-y[t]); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {5 e^{10 t}}{e^{10 t}+e^{5 c_1}}\\ y(t)&\to 0\\ y(t)&\to 5 \end{align*}

✓ Sympy. Time used: 0.240 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*(5 - y(t))*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {5}{C_{1} e^{- 10 t} + 1} \]