Finding single and multivariable integrating factors to some non-exact differential equations

Finding integrating factors is a method of solving non-exact differential equations. In this paper, the problem of finding integrating factors was stated clearly. Assumptions were made, and solutions were proposed under these assumptions. Specifically three cases were given, and then solutions were given for each case. The first two cases arrived at already existing methods. The third case described a new method for finding an integrating factor, provided some specific conditions are met. The first two cases describe methods for finding single variable integrating factors, whiles the third case describes a method for finding a multivariable integrating factor. In addition, some examples were given for the third case to demonstrate the use of the new method in finding integrating factors.