  In this study, we give the variation of parameters method from a different
viewpoint for the Nth order inhomogeneous linear ordinary difference equations
with constant coefficient by means of delta exponential function . Advantage of
this new approachment is to enable us to investigate the solution of difference
equations in the closed form. Also, the method is supported with three
difference eigenvalue problems, the second-order Sturm-Liouville problem, which
is called also one dimensional Schr\"odinger equation, having Coulomb
potential, hydrogen atom equation, and the fourth-order relaxation difference
equations. We find sum representation of solution for the second order discrete
Sturm-Liouville problem having Coulomb potential, hydrogen atom equation, and
analytical solution of the fourth order discrete relaxation problem by the
variation of parameters method via delta exponential and delta trigonometric
functions .
