Construction of Normal-Regular Solutions of Inhomogeneous System of Partial Differential Equations of Second Order

In this paper, we consider an inhomogeneous system of second-order partial differential equations with regular singularities at the point (0, 0). The Frobenius-Latysheva method is used to find normally regular solutions. A universal approach to constructing solutions in the vicinity of regular singularities has been developed, the number of linearly independent partial solutions has been determined, and compatibility and integrability conditions have been investigated. Concrete examples demonstrate the use of the method of uncertain coefficients to obtain partial solutions of inhomogeneous systems.