This paper presents an alternative methodology for finding the solution of the boundary value problem (BVP) for the linear partial differential operator. We are particularly interested in the linear operator ⊕k, where ⊕k=♡k♢k, ♡k is the biharmonic operator iterated k-times and ♢k is the diamond operator iterated k-times. The solution is built on the Green’s identity of the operators ♡k and ⊕k, in which their derivations are also provided. To illustrate our findings, the example with prescribed boundary conditions is exhibited.