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Mubeen [5] has recently introduced the second order linear differential equations of k-hypergeometric and confluent k-hypergeometric functions. The main objective of this present paper is to develop these k-hypergeometric and confluent k-hypergeometric differential equations by adopting the same method, used by Rainville in [6]. Also, we find out the solutions of the form w= 2 F1, k ((α, k),(β, k);(γ, k); z) and w= 1 F1, k ((α, k);(β, k); z) of khypergeometric and confluent k-hypergeometric differential equations respectively, in the same way.