64.25.3 problem 3

Internal problem ID [13627]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 13, Limit cycles and periodic solutions. Section 13.4, Exercises page 706
Problem number : 3
Date solved : Monday, March 31, 2025 at 08:03:05 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x&=0 \end{align*}

✗ Maple

ode:=diff(diff(x(t),t),t)+x(t)^4*diff(x(t),t)-diff(x(t),t)+x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],{t,2}]+x[t]^4*D[x[t],t]-D[x[t],t]+x[t]==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)**4*Derivative(x(t), t) + x(t) - Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : The given ODE -(-x(t) - Derivative(x(t), (t, 2)))/(x(t)**4 - 1) + Derivative(x(t), t) cannot be solved by the factorable group method