CONSTRUCTION OF INHOMOGENEOUS SYSTEM SOLUTIONS FOR DIFFERENTIAL
EQUATIONS IN PARTIAL THIRD-ORDER HYPERGEOMETRIC TYPE
Abstract
For consideration introduced inhomogeneous near the singularity (0, 0)
little-studied regular system consisting of two third-order partial
differential equations. Distinctive features of constructing a general
solution of an inhomogeneous system are installed. A number of specific
systems are highlighted from the corresponding generalized homogeneous
system of hypergeometric form. For them established a common method for
constructing a solution and have been determined the number of linearly
independent particular solutions, at the same time regularity conditions
are found near the singularity (0, 0) and compatibility conditions as
well as integrability. The Frobenius-Latysheva method shows the features
of constructing general and particular solutions of a homogeneous
Clausen system. Constructing a general and particular solutions of
nonhomogeneous system Clausen and one partial differential equation of
the third order obtained by adding the two equations nonhomogeneous
system shown Clausen method of undetermined coefficients.