ИСТИНА

Using the example of a polynomial resonance case of the Bautin system with parameters, we have written out the conditions for local integrability near stationary points and found restrictions on the parameters under which these conditions are satisfied. The resulting constraint is written as a system of algebraic equations for the ODE parameters. It is shown that for parameter values that are solutions of such an algebraic system, the ODE turns out to be integrable. In this way we have found several cases of integrability. We propose a heuristic method that allows one to a priory determine the cases of integrability of an autonomous ODE with a polynomial right-hand side. The paper has an experimental character.