70.1.16 problem 2.4 (iii)

Internal problem ID [14235]
Book : Nonlinear Ordinary Differential Equations by D.W.Jordna and P.Smith. 4th edition 1999. Oxford Univ. Press. NY
Section : Chapter 2. Plane autonomous systems and linearization. Problems page 79
Problem number : 2.4 (iii)
Date solved : Monday, March 31, 2025 at 12:13:37 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+x^{\prime }+x-x^{3}&=0 \end{align*}

✗ Maple

ode:=diff(diff(x(t),t),t)+diff(x(t),t)+x(t)-x(t)^3 = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve -x(t)**3 + x(t) + Derivative(x(t), t) + Derivative(x(t), (t, 2))