Studying the focal value of ordinary differential equations by normal form theory

Abstract

We present a new method to calculate the focal value of ordinary differential equation by applying the theorem defined the relationship between the normal form and focal value, with the help of a symbolic computation language MATHEMATICA, and extending the matrix representation method. This method can be used to calculate the focal value of any high order terms. This method has been verified by an example. The advantage of this method is simple and more readily applicable, the result is directly obtained by substitution.