68.4.69 problem 66

Internal problem ID [17249]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 66
Date solved : Thursday, October 02, 2025 at 01:59:54 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=16 y-8 y^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(y(t),t) = 16*y(t)-8*y(t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {2}{1+2 \,{\mathrm e}^{-16 t} c_1} \]

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 42

ode=D[y[t],t]==16*y[t]-8*y[t]^2; 
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]-2) K[1]}dK[1]\&\right ][-8 t+c_1]\\ y(t)&\to 0\\ y(t)&\to 2 \end{align*}

✓ Sympy. Time used: 0.233 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(8*y(t)**2 - 16*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {2}{C_{1} e^{- 16 t} + 1} \]