38.3.8 problem 14

Internal problem ID [8275]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 05:21:15 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \left (y-3\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

\[ y = \frac {3}{1+3 \,{\mathrm e}^{3 x} c_1} \]

✓ Mathematica. Time used: 0.111 (sec). Leaf size: 40

ode=D[y[x],x]==y[x]*(y[x]-3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-3) K[1]}dK[1]\&\right ][x+c_1]\\ y(x)&\to 0\\ y(x)&\to 3 \end{align*}

✓ Sympy. Time used: 0.197 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {3 C_{1}}{C_{1} - e^{3 x}} \]