72.30.1 problem 4 (a)

Internal problem ID [19773]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 11. Nonlinear Equations. Section 64. Periodic Solutions. The PoincareBendixson Theorem. Problems at page 570
Problem number : 4 (a)
Date solved : Thursday, October 02, 2025 at 04:42:09 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5}&=0 \end{align*}

✗ Maple

ode:=diff(diff(x(t),t),t)+(5*x(t)^4-9*x(t)^2)*diff(x(t),t)+x(t)^5 = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],{t,2}]+(5*x[t]^4-9*x[t]^2)*D[x[t],t]+x[t]^5==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 - 9*x(t)**2)*Derivative(x(t), t) + x(t)**5 + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : The given ODE Derivative(x(t), t) - (-x(t)**5 - Derivative(x(t), (t, 2)))/((5*x(t)**2 - 9)*x(t)**2) cannot be solved by the factorable group method