In this work, we studied that power series method is the standard basic method for solving linear differential equations with variable coefficients. The solution usually take the form of power series; this explain the name power series method. We review some special second order ordinary differential equations. Power series method is described at ordinary point as well as at singular points (which can be removed called Frobenius method) of differential equations. The Frobenius method extends the simple series method to include negative and fractional powers and it also allows a natural extension involving logarithm terms. Few examples are presented on this method by solving special second order ordinary differential equations.