I have the following ODE:
$$\dot x=-y(x^2+y^2), \dot y=x(x^2+y^2)$$
I want to sketch the phase portrait (manually) and I want to find the flow $\phi_t$, the orbit $O(x_0)$ and the limit set $\omega(x_0)$
I start by taking polar coordinates and change the system to $\dot r=-r^3\sin\theta, \dot\theta=r^3\cos\theta$
The phase portrait then looks like the one a stable centre, right?
How can I continue to find the flow of the function, i.e the solution of the differential equation?