64.25.1 problem 1

Internal problem ID [13696]
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 : 1
Date solved : Tuesday, January 28, 2025 at 05:55:23 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=4 x \left (t \right )-4 y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )+4 y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \end{align*}

✗ Solution by Maple

dsolve([diff(x(t),t)=4*x(t)-4*y(t)-x(t)*(x(t)^2+y(t)^2),diff(y(t),t)=4*x(t)+4*y(t)-y(t)*(x(t)^2+y(t)^2)],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved