Abstract
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this defect, we introduce in this paper, new general formulas and their related recurrence relations for computing the differential transform of any analytic nonlinear non-autonomous function with one or multi-variable. Several test examples for different types of nonlinear differential and integro-differential equations are solved to demonstrate the applicability and validity of the present method. The obtained results declare that the suggested approach not only effective but also a straightforward and powerful for solving differential and integro-differential equations with complex nonlinearities.