The differential transform method (DTM) for solving linear and nonlinear higher order differential equations especially which arising in the field of electric circuit problems is used. In almost cases, DTM gives the series of solutions which can be easily converted to exact ones. In nonlinear problems it is useful to use the Adomian polynomial to overheads the nonlinear terms. Some illustrative examples are presented with some RLC circuit problems to show the simplicity and accuracy of the used method compared with other numerical methods. All calculations are made with the help of computer algebra software Mathematica 11.2.