We define the system
$$\begin{cases}\dot{x}=P(x,y) \\\dot{y}=Q(x,y)\end{cases}$$
with $P(x,y)$, $Q(x,y)$ polinomyals with degree $\leq 3$.
How can we find the general form of the family of systems that have an isochrone center?
On my notes we barely defined them, and it's written that it's a little bit difficult to find this set of differential equations. Is there any way to give a general form of systems with an isochrone center?
Thanks.