44.4.39 problem 21

Internal problem ID [7052]
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 : 21
Date solved : Sunday, March 30, 2025 at 11:36:40 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.177 (sec). Leaf size: 29

ode=D[y[x],x]==y[x]^2-3*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {3}{1+e^{3 (x+c_1)}} \\ y(x)\to 0 \\ y(x)\to 3 \\ \end{align*}

✓ Sympy. Time used: 0.370 (sec). Leaf size: 12

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

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