72.3.6 problem 6

Internal problem ID [14670]
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 1.4 page 61
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 06:47:06 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.227 (sec). Leaf size: 21

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

\[ w = \frac {3 \,{\mathrm e}^{4 t}-3}{3+{\mathrm e}^{4 t}} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 23

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

\[ w(t)\to \frac {3 \left (e^{4 t}-1\right )}{e^{4 t}+3} \]