Summary: In this paper, method is offered enabling reduction of resolving system of heterogeneous partial-derivative differential equations of the sixteenth order within the variant of mathematical theory of non-thin shallow shells to the differential equations of the second and fourth orders. A method is used of geometrical parameters perturbation and symbolical method.

Keywords: variant of mathematical theory, non-thin shallow shell, system of heterogeneous partial-derivative differential equations, method of perturbations, operator.

Abstract: As well as analyzing equations of fourth and sixth order, the article suggests a method allowing non-homogeneous partial differential equations of even order in mathematical theory of plates to be reduced to non-homogeneous equations of second order which could be solved using the Hankel integral transform.

Keywords: reduction of order, non-homogeneous partial differential equation, mathematical theory, plate.