Perhaps a substitution of the form , giving
Since the variables have been separated, you can now solve using integration.
Every first order equation, however, has an "integrating factor". Here, that integrating factor is . Multiplying that equation by gives . (Notice that this is now clearly in terms of so Prove It's substitution works.)
The derivative of , with respect to y, is and the derivative of , with respect to x, is also .
That means that there exist a function, F(x,y), such that .
Since , for some function, g, of y only. Differentiating that with respect to y, so that . That is, and since "dF= 0" means that F is a constant, the solution to the differential equation is .