THE COORDINATED SOLUTION OF TWO DIFFERENTIAL EQUATIONS IN PRIVATE DERIVATIVES OF THE THIRD ORDER

Аннотация

In the study the possibility of constructing a solution near a variety of special features of the system
consisting of two differential equations in partial derivatives of the third order was investigated. There definitive
aspects of such systems in comparison with systems consisting of two differential equations in partial derivatives of
second order were established. The classification of regular and irregular singularities was carried out, the relevant
solutions are constructed. A specific example shows that the application of the Frobenius - Latysheva method to the
construction of a solution of a degenerate hypergeometric system consisting of two third-order partial differential
equations. A variety of properties of system solution were considered, which shows that these solutions have the
properties of generalized hypergeometric functions.