74.4.38 problem 38

Internal problem ID [15860]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 38
Date solved : Monday, March 31, 2025 at 02:08:57 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.042 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.209 (sec). Leaf size: 40

ode=D[y[t],t]==y[t]^3-y[t]^2; 
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: 0.318 (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)
 

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