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## Scientific Bulletin. Physical and Mathematical Research

#### Abstract

For the elliptic type of differential equation with two singular coefficients, the quadratic values of the Dirixle and Dirixle-Neumann problems were found in the quarter in that work. The field and boundary conditions for solving these problems are described in the polar coordinate system. The result is a rectangle in the polar coordinate system. Then, we used the method of separating variables in the right rectangle, that is, divided the variables by the equation and divided the problem into two distinct values for ordinary differential equations. The first of the ordinary differential equations is the substitution of , where the equation , Bessel equation is presented, and the general solution of the first equation is found using the equation that represents the general solution of this equation. The general solution of the problem is found by submitting to the conditions of the first problem, and the specific values and corresponding functions of the first problem for ordinary differential equations are found. In the second ordinary differential equation, the substitution of was performed and the equation is referred to the equation known as Gaussian hypergeometric equation. Using the general solution of this equation around the zero point and the substitution, the general solution of the second ordinary differential equation is found. Submitting this general solution to the conditions of the second problem, we find the specific values and corresponding functions of the second problem for ordinary differential equations. After the first and second problems of the ordinary differential equations have been found, they are put into the equation and are considered as the specific functions of the Dirixle problem for the singular derivative differential equation with two singular coefficients. In the same way the Dirichle-Neumann problem was investigated. Here, the equation and boundary conditions are described in a polar coordinate system. The variables are separated and the problem of the polar coordinate system is about the value inherent in ordinary differential equations. Specific values and related functions have been found for these issues. The specific functions found are put in the equation, resulting in specific functions of the Dirichle-Neumann problem.

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