THE BOUNDARY VALUE PROBLEM FOR THE DEGENERATING DIFFERENTIAL EQUATION WITH THE DEVIATING ARGUMENT
The paper formulates a boundary-value problem for a second-order degenerate heterogeneous ordinary differential equation with deviating argument. Argument deviation in the equation is of an evolutive character. The equation is considered at an origin-symmetric interval. Besides, in the point t = 0, the initial differential equation degenerates into a functional equation. Solution of the problem is found in the form of a fourth-degree polynomial. The paper demonstrates that the problem of finding coefficients of a polynomial determining the solution of the problem is reduced to a question of solvability of corresponding system of algebraic equations. After presenting the system in a matrix form, the condition ensuring existence of a single solution of the systemwas established. This resulted in obtaining an analytical solution of the initial problem, belonging to the required function class. The solution found allowscarrying out of a numerical analysis of a problem with the subsequent visualization of the solution.