The Exact Differentiail Equation and the Method of Intergrating Factor

In the process of forming the ordinary differential equation theory, many methods appeared in finding a solution of differential equation of first order, such as the separation of variables, replacement factor, etc. Among these methods, the method of integrating factoris the latest but the most effective.This paper disusses the significant role of the method of integrating factor in finding the solution of differential equation of first order,and the methods of finding the integrating factor of common first order equations.