72.5.2 problem 1 and 13 (ii)

Internal problem ID [14688]
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 (ii)
Date solved : Tuesday, January 28, 2025 at 07:11:26 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (-2\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 18

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

\[ y = -\frac {2}{3 \,{\mathrm e}^{12+6 t}-1} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 20

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

\[ y(t)\to \frac {2}{1-3 e^{6 (t+2)}} \]