72.5.39 problem 37 (viii)

Internal problem ID [14725]
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)
Date solved : Tuesday, January 28, 2025 at 07:12:49 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 1.327 (sec). Leaf size: 20

dsolve(diff(y(t),t)=y(t)^2-y(t)^3,y(t), singsol=all)
 

\[ y = \frac {1}{\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-t -1}}{c_{1}}\right )+1} \]

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 42

DSolve[D[y[t],t]==y[t]^2-y[t]^3,y[t],t,IncludeSingularSolutions -> True]
 

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