  The method of separation of variables is significant, it has been applied to
physics, engineering , chemistry and other fields. It allows to reduce the
diffculity of problems by separating the variables from partial differential
equation system into ordinary differential equations system. However, this
method has complexity in higher order partial differential equations. In this
reserach, we generalize this method by using multinomial theorem of n-harmonic
equation to solve n-harmonic equation with $m$ dimension and then solving an
important class of partial differential equations with unbounded boundary
conditions. Additionaly, application of convolution.
