ON AN OVERDETERMINED SYSTEM OF SECOND ORDER DIFFIRENTIAL EQUATIONS WITH SINGULAR POINT
In this paper we consider the over determined system of second order differential equations with a singular point. The system of equations (1) consists of a hyperbolic equation and one partial differential equation of second order with a singular point. The first equation of system (1) under certain conditions on the coefficients can be represented as a superposition of two first order differential operators. Solving this equation and substituting its value in the second equation, we obtain the compatibility conditions for the coefficients and right-hand sides. On the basis of the conditions of independence from the left side of the variable ??, to determine any function ??1(??), we obtain an ordinary differential equation of the first order. Another arbitrary function ??1(??) is determined from the condition of the independence of the left part at the appropriate, passing to the limit.Thus, the obtained representing the solution manifold system using a single arbitrary function of one independent variable ?? and one arbitrary constant study of properties of the solutions, as well as consider the problem of А.