ABSTRACT
This chapter focuses on the development that are ordinary differential equations, utilizing some classical approaches, which are commonly used in the current literature, for the construction of Green's functions for linear boundary value problems for ordinary differential equations (ODE). One of these approaches is associated with the proof of existence and uniqueness theorem for the Green's function. It appears that in the existing literature, this approach is more popular compared to the other one that is based on the Lagrange's method of variation of parameters. The chapter shows that the symmetry of Green's functions. Their symmetry is directly related to the so-called self-adjointness of the differential operator involved. This feature of a Green's function is of great theoretical and practical importance. The chapter describes the Green's function for a linear boundary value problem for an ODE of the nth order with variable coefficients. It explains the traditional method for the construction of Green's functions, based on their defining properties.
