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 : Wednesday, March 05, 2025 at 04:04:04 AM
CAS classification : [_quadrature]

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

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

ode:=diff(y(x),x) = y(x)-y(x)^3; 
dsolve(ode,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*}

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

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

✓ Sympy. Time used: 0.874 (sec). Leaf size: 39

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

\[ \left [ y{\left (x \right )} = - \sqrt {- \frac {e^{2 x}}{C_{1} - e^{2 x}}}, \ y{\left (x \right )} = \sqrt {- \frac {e^{2 x}}{C_{1} - e^{2 x}}}\right ] \]