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 : Monday, January 27, 2025 at 02:42:35 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==y[x]^2-3*y[x],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*}