78.30.1 problem 4 (a)

Internal problem ID [18487]
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 : Tuesday, January 28, 2025 at 11:50:45 AM
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*}

✗ Solution by Maple

dsolve(diff(x(t),t$2)+(5*x(t)^4-9*x(t)^2)*diff(x(t),t)+x(t)^5=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]^4-9*x[t]^2)*D[x[t],t]+x[t]^5==0,x[t],t,IncludeSingularSolutions -> True]
 

Not solved