Integrating Factors

The title of this article is, finding factors of integrating or integrating factors for partial equation of. In general case, finding of these factors seem difficult, but in particular cases these factors exist which are called factor of the first-order, factor of the second-order �. . . , here seven orders of factors with relevant proofs and problems are studied. Finding of integrating factors with expressions classification method also discussed, it is mentioned into two problems and in one table. is factor of the first-order. If is a function of x alone. is factor of the second-order. It is used when is a function of y alone. . is factor of the third-order. It is used when is a function of z alone. Thus. is factor of the fourth-order, if the differential equation be as follow: is factor of the fifth-order, if. is factor of the sixth-order if is a function of. is factor of the seventh-order if is a function of. For the factors of the third and fourth, �. orders, partial equation of is considered. The number of factors are more than seven, so it is prevented for not increasing the pages and it is not written.