64.25.6 problem 6

Internal problem ID [13630]
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 : 6
Date solved : Monday, March 31, 2025 at 08:03:15 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3}&=0 \end{align*}

✗ Maple

ode:=diff(diff(x(t),t),t)+(5*x(t)^4-6*x(t)^2)*diff(x(t),t)+x(t)^3 = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],{t,2}]+(5*x[t]^4-6*x[t]^2)*D[x[t],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((5*x(t)**4 - 6*x(t)**2)*Derivative(x(t), t) + x(t)**3 + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : The given ODE Derivative(x(t), t) - (-x(t)**3 - Derivative(x(t), (t, 2)))/((5*x(t)**2 - 6)*x(t)**2) cannot be solved by the factorable group method