Internal problem ID [12971]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {w^{\prime }-3 w^{3}+12 w^{2}=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 49
dsolve(diff(w(t),t)=3*w(t)^3-12*w(t)^2,w(t), singsol=all)
\[ w \left (t \right ) = {\mathrm e}^{\operatorname {RootOf}\left (\ln \left ({\mathrm e}^{\textit {\_Z}}+4\right ) {\mathrm e}^{\textit {\_Z}}+48 c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+48 t \,{\mathrm e}^{\textit {\_Z}}+4 \ln \left ({\mathrm e}^{\textit {\_Z}}+4\right )+192 c_{1} -4 \textit {\_Z} +192 t -4\right )}+4 \]
✓ Solution by Mathematica
Time used: 0.392 (sec). Leaf size: 50
DSolve[w'[t]==3*w[t]^3-12*w[t]^2,w[t],t,IncludeSingularSolutions -> True]
\begin{align*} w(t)\to \text {InverseFunction}\left [\frac {1}{4 \text {$\#$1}}+\frac {1}{16} \log (4-\text {$\#$1})-\frac {\log (\text {$\#$1})}{16}\&\right ][3 t+c_1] \\ w(t)\to 0 \\ w(t)\to 4 \\ \end{align*}