Finding New Integrals of the Algaba System

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[2] and on the computation of the resonant normal form[3, 4]. For the partial non Hamilton 5-parameter case of concrete planar system[1], 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[5]. But along the hyper plane b2 = 2/3 there can exist additional such subsets[6]. We have found two more first integrals of motion.