72.2.7 problem 7

Internal problem ID [14642]
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 1.3 page 47
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 06:45:56 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 y \left (1-y\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 20

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

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