72.5.21 problem 8

Internal problem ID [14707]
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 : Tuesday, January 28, 2025 at 07:12:10 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.187 (sec). Leaf size: 49

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

\[ w = {\mathrm e}^{\operatorname {RootOf}\left (\ln \left ({\mathrm e}^{\textit {\_Z}}+4\right ) {\mathrm e}^{\textit {\_Z}}+48 c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+48 t \,{\mathrm e}^{\textit {\_Z}}+4 \ln \left ({\mathrm e}^{\textit {\_Z}}+4\right )+192 c_{1} -4 \textit {\_Z} +192 t -4\right )}+4 \]

✓ Solution by Mathematica

Time used: 0.222 (sec). Leaf size: 42

DSolve[D[w[t],t]==3*w[t]^3-12*w[t]^2,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*}