Considering the importance of teaching linear differential equations, it can be said that every physical and technical phenomenon, which is expressed and modeled in mathematical sciences, is a differential equation. Differential equations are essential part of contemporary comparative mathematics that covers all fields of physics (heat, mechanics, atoms, electronics, magnetism, light and waves), many economic subjects, engineering subjects, natural problems, population growth and technical problems today. In this article, we will consider the theory of linear inhomogeneous differential equations of the third order with boundary conditions and the transformation of coefficients into multiple functions. In the field of differential equations, a boundary value problem with a set of additional constraints is called boundary value problem. The solution of this boundary value problem is actually a solution for the differential equation with the given constraints, which actually satisfies the conditions of the boundary value problem. Differential equation problems with boundary conditions are similar to initial value problems. A boundary value problem with conditions defined on the boundaries is an independent variable in the equation, while an initial value problem is defined as the same condition that has the value of the independent variable and this value is less than the limit, hence the term value is initial and the initial value is the amount of data that matches the minimum or maximum input, internal, or output value specified for a system or component. When the boundaries of the boundary values in the solution of obtaining the constants of the third order differential equation , and are determined, the failure to obtain the constants is called the boundary problem. We solve this problem by considering the given conditions for the real Green's function. Every real function is a solution of a set of linear differential equations, and the values of its boundary value depend on the intervals.
Green's function, boundary value problem, private solution, general solution
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