74.4.69 problem 66

Internal problem ID [15962]
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 : Tuesday, January 28, 2025 at 08:24:53 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.221 (sec). Leaf size: 42

DSolve[D[y[t],t]==16*y[t]-8*y[t]^2,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*}