66.5.39 problem 37 (viii)

Internal problem ID [16012]
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 : Thursday, October 02, 2025 at 10:38:41 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 20

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

\[ y = \frac {1}{\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-1-t}}{c_1}\right )+1} \]

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 42

ode=D[y[t],t]==y[t]^2-y[t]^3; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.183 (sec). Leaf size: 19

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

\[ t + \log {\left (y{\left (t \right )} - 1 \right )} - \log {\left (y{\left (t \right )} \right )} + \frac {1}{y{\left (t \right )}} = C_{1} \]