44.4.37 problem 19

Internal problem ID [7050]
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 : 19
Date solved : Monday, January 27, 2025 at 02:42:29 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

\begin{align*} y &= \frac {1}{\sqrt {c_{1} {\mathrm e}^{-2 x}+1}} \\ y &= -\frac {1}{\sqrt {c_{1} {\mathrm e}^{-2 x}+1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.649 (sec). Leaf size: 100

DSolve[D[y[x],x]==y[x]-y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {e^x}{\sqrt {e^{2 x}+e^{2 c_1}}} \\ y(x)\to \frac {e^x}{\sqrt {e^{2 x}+e^{2 c_1}}} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ y(x)\to -\frac {e^x}{\sqrt {e^{2 x}}} \\ y(x)\to \frac {e^x}{\sqrt {e^{2 x}}} \\ \end{align*}