**ABSTRACT**

The recently proposed core-shell approach for solving differential equations is applied to find solutions of difference equations for the first time. The new method provides an alternative to the existing methods in search of analytical solutions of difference equations. The method is applied mainly to homogenous and non-homogenous variable coefficient second order linear difference equations. Some theorems on the general form of the solutions are given for such equations. Finally, the Cauchy-Euler difference equation is solved by the method. For higher order variable coefficient difference equations, solutions can be constructed in an analogous way. For first and second order equations, the general solutions given in theorems can directly be implemented to find the solutions for the specific equations. The analysis presented will not only provide an alternative solution method, but will also add insight to the understanding of difference equations and the nature of solutions.

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