Chapter 7.5, Problem 9P

Determine the periodic solutions, if any, of the system

$\frac{dx}{dt}=-y+\frac{x}{\sqrt{x^2+y^2}}\left(x^2+y^2-5\right)$

$\frac{dx}{dt}=x+\frac{y}{\sqrt{x^2+y^2}}\left(x^2+y^2-5\right)$