  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 a new general formula and its related
recurrence relations for computing the differential transform of any analytic
nonlinear non-autonomous function with one or multi-variable. Regarding, the
formula in the literature was found not applicable to deal with the present
non-autonomous functions. Accordingly, a generalization is presented in this
paper which reduces to the corresponding formula in the literature as a special
case. Several test examples for different types of nonlinear differential and
integro-differential equations are solved to demonstrate the validity and
applicability of the present method. The obtained results declare that the
suggested approach not only effective but also a straight forward even in
solving differential and integro-differential equations with complex
nonlinearities.
