The Generalized form of the Almansi’s theorem can be found in solid mechanics. For example in the solution of the transversely isotropic and orthropic media mechanics, the theorem are encountered. Hence its solution is a must in applied mathematics.
In this paper the homogenous solution is found by transforming the order of the partial differential from 2n to n differential equation with second order which can be solved easily. The method is verified in some simple cases where their solution is existed.