38.5.51 problem 47 (a)

Internal problem ID [8399]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 47 (a)
Date solved : Tuesday, September 30, 2025 at 05:34:45 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.110 (sec). Leaf size: 16

ode:=diff(y(x),x) = y(x)-y(x)^3; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2}{\sqrt {4-3 \,{\mathrm e}^{-2 x}}} \]

✗ Mathematica

ode=D[y[x],x]==y[x]-y[x]^3; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.570 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \sqrt {- \frac {e^{2 x}}{\frac {3}{4} - e^{2 x}}} \]