The Frobenius Method for Solving Ordinary Differential Equation with Coefficient Variable

One of the problems in differential equation is to get solution of Ordinary differential equation with coefficient variable. So that needed a method to solve it, it is the series solution. The series solution at point t can be used if t 0 is ordinary point of ordinary differential equations, but if t 0 is singular point, it is needed an extend series solution which called Frobenius method. This research aims to determine the form of extend series solution at singular points and the form of linear independently second solutions. The results of this research indicate the form of extend series solution at singular point and then based on roots of indicial terms, there are three kinds linear independently second solution where distinct roots not differing by an integer, roots differing by an integer, and double root.