64.25.6 problem 6

Internal problem ID [13701]
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 : Tuesday, January 28, 2025 at 05:55:34 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*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[x[t],{t,2}]+(5*x[t]^4-6*x[t]^2)*D[x[t],t]+x[t]^3==0,{x[t]},t,IncludeSingularSolutions -> True]
 

Not solved