In this project, we propose two methods -- 1-D differential transform and 2-D differential transform -- to engage in the basic study on non-homogeneous plate vibration problems. Non-uinform plate vibration problems commonly exit in engineering fields. Because the governing equation of non-uinform plate vibration problems is a P.D.E. with variable coefficients, the closed form solution is not available. In the past, the problems were mainly solved by numerical methods and approximate methods. The solutions obtained by the numerical methods usually undergo a lot of computer computations and require a lot of CPU time. The solutions obtained by the approximate methods usually undergo complicated derivations. However, using the proposed method, we simplify the solving processes and obtain the series form solutions. Besides using 1-D and 2-D Differential transform method to do researches mentioned above, we write softwares for instruction to provide an easier way to study the non-uniform plate vibration problems for those student with poor mathematic background.