About a Special Second-Order Functional Differential Equation

When searching for solutions to boundary value, initial, or mixed problems for degenerate functional differential equations, second-order differential equations naturally arise (especially when part of the boundary of the domain of the equation is freed from boundary conditions). A method for reconstructing one type of hyperbolic equation with variable coefficients from its general solution is shown. For partial differential equations, the general solution can be found much less frequently and the situation here is more complicated. Individual hyperbolic type equations admit general solutions in the form of a sum of traveling waves. Mathematical models of many technical and engineering problems force us to consider more general hyperbolic equations with variable coefficients. It is rarely possible to find a general solution to such equations using previously known methods.