Value problem for the first kind of linear second order differential equations with deviating argument on balanced segment

Modelling of engineering and economic, biological, and medical and other applications makes it necessary to study problems for ordinary differential equations and partial differential equations.We study the unique solvability of the boundary value problem for first order ordinary linear second-order differential equation with deviating argument on a symmetric interval. Using the symmetry of the segment, which solved the boundary value problem, the solution is sought in the form of a sum of even and odd functions. With this approach, the solution is reduced to the study of the question of solvability of classical boundary value problems for even or odd components of unknown function that allows you to set conditions for the unique solvability depending on the input data. Properties auxiliary task allowed to establish spectrum investigated boundary value problem.