50.4.63 problem 60

Internal problem ID [10238]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 60
Date solved : Tuesday, September 30, 2025 at 07:13:01 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \left (1-y^{2}\right ) \end{align*}

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

ode:=diff(y(x),x) = y(x)*(1-y(x)^2); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {{\mathrm e}^{-2 x} c_1 +1}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{-2 x} c_1 +1}} \\ \end{align*}

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 53

ode=D[y[x],x]==y[x]*(1-y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1] (K[1]+1)}dK[1]\&\right ][-x+c_1]\\ y(x)&\to -1\\ y(x)&\to 0\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.707 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((y(x)**2 - 1)*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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