ИСТИНА

The paper investigates the connection between the global integrability of an autonomous two-dimensional polynomial ODE system and its local integrability near stationary points using the example of the polynomial case of a Lenard-type equation. We presented the equation in the form of a dynamical system and parametrized it. The conditions for local integrability near stationary points are written out and the values of the parameters under which these conditions are satisfied are found. It is established that for certain values of the parameters obtained in this way, the system actually turns out to be integrable. Thus, we can speak of a heuristic approach that allows one to determine the cases of ODE integrability.