Solution of One Spectral Problem for a Mixed Type Equation

Abstract

In this article, we consider the spectral problem for a mixed-type equation in the one-dimensional case. This means that the equation contains both differential and integral terms. Using the method of separation of variables, we can solve these equations independently. For an equation containing the variable x, we obtain a system of linear ordinary differential equations with running coefficients. And for an equation containing the variable t, we obtain a simple ordinary differential equation. Using the method of separation of variables allows us to reduce the original spectral problem for a mixed-type equation to a system of ordinary differential equations, which can be easily solved to find the eigenvalues and eigenfunctions.