90.3.17 problem 17

Internal problem ID [25081]
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 : 17
Date solved : Thursday, October 02, 2025 at 11:49:35 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=4 y-y^{2} \end{align*}

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

ode:=diff(y(t),t) = 4*y(t)-y(t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {4}{1+4 \,{\mathrm e}^{-4 t} c_1} \]

✓ Mathematica. Time used: 0.165 (sec). Leaf size: 36

ode=D[y[t],{t,1}] ==4*y[t]-y[t]^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {4 e^{4 t}}{e^{4 t}+e^{4 c_1}}\\ y(t)&\to 0\\ y(t)&\to 4 \end{align*}

✓ Sympy. Time used: 0.229 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
n = symbols("n") 
m = symbols("m") 
y = Function("y") 
ode = Eq(y(t)**2 - 4*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {4}{C_{1} e^{- 4 t} + 1} \]