THE DEGENERATION OF THE SYSTEMS OF THE NONLINEAR EQUATIONS IN QUOTIENT DERIVED 2- ORDER WITH SINGULARS FACTOR

Abstract

In this paper, we consider a system of three nonlinear equations with three singular coefficients. We study their compatibility conditions for the systems under study. Then there are some functions where they may be particular or special solutions of the system. Otherwise, we get that these systems will not be compatible. The goal of the work is to find the manifolds of solutions of system (1), the conditions, the compatibility of which are fulfilled identically. To find solutions to the problem, by making a replacement, we transform the original systems to the system of equations in full first-order differentials, find the solutions of the latter systems and the variety of their solutions. As a result of the integration of the systems, it was obtained that in what cases, and at what values, the n-solution of the original systems is continuous, and in other cases it is singular, moreover, the order of the singularity is shown.