ИСТИНА

We consider an autonomous system of ordinary differential equations, which is resolved with respect to derivatives. To study local integrability of the system near a degenerate stationary point, we use an approach based on Power Geometry\cite{Bruno:1998} and on the computation of the resonant normal form\cite{Bruno:1979,Edneral:2007}. For the partial non Hamilton 5-parameter case of concrete planar system\cite{Algaba:2009}, we found the complete set of necessary conditions on parameters of the system for which the system is locally integrable near a degenerate stationary point. These sets of parameters, satisfying the conditions, consist of 4 two-parameter subsets in this 5-parameter space. The first integral of motion corresponds of each such subset\cite{Edneral:2011}. But along the hyper plane $b^2 = 2/3$ there can exist additional such subsets\cite{Edneral:2013}. We have found two more first integrals of motion.