38.4.40 problem 22

Internal problem ID [8339]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 22
Date solved : Tuesday, September 30, 2025 at 05:29:12 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.045 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 7

ode=D[y[x],x]==y[x]^2-y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \end{align*}

✓ Sympy. Time used: 0.176 (sec). Leaf size: 19

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

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