64.25.5 problem 5

Internal problem ID [13700]
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 : 5
Date solved : Tuesday, January 28, 2025 at 05:55:29 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✗ Solution by Maple

dsolve(diff(x(t),t$2)+(x(t)^4+x(t)^2)*diff(x(t),t)+x(t)^3+x(t)=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}]+(x[t]^4+x[t]^2)*D[x[t],t]+x[t]^3+x[t]==0,{x[t]},t,IncludeSingularSolutions -> True]
 

Not solved