In this problem we consider an equation in differential form M dx + N dy = 0. The equation in differential form M dx + dy = 0 is not exact. Indeed, we have M - = For this exercise we can find an integrating factor which is a function of a alone since M - N. N can be considered as a function of alone. N = (6xye - 4e* sin(x) + 5e) dx + (6xye 5)dy = 0 Namely we have (x) Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where M = Which is exact since My = N = = = are equal. This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where F(x, y) =