66.5.21 problem 8

Internal problem ID [15994]
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 : 8
Date solved : Thursday, October 02, 2025 at 10:38:05 AM
CAS classification : [_quadrature]

\begin{align*} w^{\prime }&=3 w^{3}-12 w^{2} \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 49

ode:=diff(w(t),t) = 3*w(t)^3-12*w(t)^2; 
dsolve(ode,w(t), singsol=all);
 

\[ w = {\mathrm e}^{\operatorname {RootOf}\left (\ln \left ({\mathrm e}^{\textit {\_Z}}+4\right ) {\mathrm e}^{\textit {\_Z}}+48 c_1 \,{\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+48 t \,{\mathrm e}^{\textit {\_Z}}+4 \ln \left ({\mathrm e}^{\textit {\_Z}}+4\right )+192 c_1 -4 \textit {\_Z} +192 t -4\right )}+4 \]

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 42

ode=D[w[t],t]==3*w[t]^3-12*w[t]^2; 
ic={}; 
DSolve[{ode,ic},w[t],t,IncludeSingularSolutions->True]
 

\begin{align*} w(t)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-4) K[1]^2}dK[1]\&\right ][3 t+c_1]\\ w(t)&\to 0\\ w(t)&\to 4 \end{align*}

✓ Sympy. Time used: 0.254 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
w = Function("w") 
ode = Eq(-3*w(t)**3 + 12*w(t)**2 + Derivative(w(t), t),0) 
ics = {} 
dsolve(ode,func=w(t),ics=ics)
 

\[ t - \frac {\log {\left (w{\left (t \right )} - 4 \right )}}{48} + \frac {\log {\left (w{\left (t \right )} \right )}}{48} - \frac {1}{12 w{\left (t \right )}} = C_{1} \]