64.25.4 problem 4

Internal problem ID [13699]
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 : 4
Date solved : Tuesday, January 28, 2025 at 05:55:27 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x&=0 \end{align*}

✗ Solution by Maple

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

Not solved