64.25.3 problem 3

Internal problem ID [13698]
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 : 3
Date solved : Tuesday, January 28, 2025 at 05:55:24 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x&=0 \end{align*}

Solution by Maple

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

Not solved