Internal problem ID [12669]
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: 37 (viii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{2}+y^{3}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 20
dsolve(diff(y(t),t)=y(t)^2-y(t)^3,y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-t -1}}{c_{1}}\right )+1} \]
✓ Solution by Mathematica
Time used: 0.408 (sec). Leaf size: 40
DSolve[y'[t]==y[t]^2-y[t]^3,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [\frac {1}{\text {$\#$1}}+\log (1-\text {$\#$1})-\log (\text {$\#$1})\&\right ][-t+c_1] y(t)\to 0 y(t)\to 1 \end{align*}