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 and on the computation of the resonant normal form. For the particular non-Hamilton 5-parameter case of concrete planar system, we found previously the almost 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 except 1 special hyper plane $b^2 = 2/3$. We wrote down 4 first integrals of motion as functions of the system parameters. Here we have proved that the limitation $b^2\neq 2/3$ can be excluded from the previously obtained solutions. Now we have not found the additional first integrals.