The purpose of this research is to present the steps of one-dimensional differential transformation method (DTM) to find the series solutions for the vibrations of a circular membrane under the specified initial and boundary conditions. The problems will be studied in the both cases of vibrations depending only on radius and of the vibrations depending on both radius and angle. We illustrate four examples of problems which the exact solutions can be solve analytically and compare them to the DTM results, to show that the DTM is reliable and of high accuracy. This work shows that the DTM is easier to use than the analytical method from the point of view of programming.

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