INCEPTION OF GREEN FUNCTION FOR THE THIRD-ORDER LINEAR DIFFERENTIAL EQUATION THAT IS INCONSISTENT WITH THE BOUNDARY PROBLEM CONDITIONS

Abstract

Regarding the importance of teaching linear differential equations, it should be noted that every physical and technical phenomenon, when expressed in mathematical sciences, is a differential equation. Differential equations are an essential part of contemporary comparative mathematics that covers all disciplines of physics (heat, mechanics, atoms, electricity, magnetism, light and wave), many economic topics, engineering fields, natural issues, population growth and today’s technical issues. Used cases. In this paper, the theory of third-order heterogeneous linear differential equations with boundary problems and transforming coefficients into multiple functions p(x) we will consider. In mathematics, in the field of differential equations, a boundary problem is called a differential equation with a set of additional constraints called boundary problem conditions. A solution to a boundary problem is a solution to the differential equation that also satisfies the boundary conditions. Boundary problem problems are similar to initial value problems. A boundary problem with conditions defined at the boundaries is an independent variable in the equation, while a prime value problem has all the conditions specified in the same value of the independent variable (and that value is below the range, hence the term "initial value"). A limit value is a data value that corresponds to the minimum or maximum input, internal, or output value specified for a system or component. When the boundaries of boundary values in the solution of the equation to obtain constants D1, D2, D3 to lay down Failure to receive constants is called a boundary problem. We solve this problem by considering the conditions given for that true Green expression function. Every real function of the solution of a set of linear differential equations holds, and its boundary values depend on the distances. Key words: Green Function, Boundary Problem, Private Solution, Public Solution, Wronskian Determinant.