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Abstract
In recent years, new formulas of the two-dimensional differential transform have been proven by using the definition of the transform. In this work, we use a new approach based on the definition of the transform and the summation properties to prove the two-dimensional differential transform of the product of two functions, then we used this result to establish other useful formulas. This study shows that this procedure can be used to find formulas for many complicated terms. This enables us to apply the differential transform method on many types of partial differential equations. To demonstrate this approach, we applied the dimensional differential transform method on selected equations and compared our results with analytical solutions obtained by other methods
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