72.5.1 problem 1 and 13 (i)

Internal problem ID [14687]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number : 1 and 13 (i)
Date solved : Tuesday, January 28, 2025 at 07:11:24 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 y \left (y-2\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 14

dsolve([diff(y(t),t)=3*y(t)*(y(t)-2),y(0) = 1],y(t), singsol=all)
 

\[ y = \frac {2}{1+{\mathrm e}^{6 t}} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 16

DSolve[{D[y[t],t]==3*y[t]*(y[t]-2),{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {2}{e^{6 t}+1} \]