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I have the following ODE:

$ \frac{dy}{dz} + \frac{y(x+y)}{(y-x)(2x+2y+z)} = 0$

where z is a function of x and y, i.e. $z(x,y)$.

For an example in two variables, I used integrating factor but I can't seem to separate this enough to do that. Do I need to simplify the expression, or use some substitution?

Any suggestions appreciated.

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At this point, you have a general scalar ordinary differential equation of the form $\frac{dy}{dx} + f(x,y) = 0$. For example, the expression $\frac{y(x+y)}{(y-x)(2x+2y+z(z,y))}$ is really of this form. There are no general methods for finding closed form solutions for such problems. –  Hans Engler Nov 25 '12 at 18:02
    
Thanks for your reply. It may be just a case of trial and error. –  Sarah24 Nov 25 '12 at 19:19
    
See my solution for your other problem. –  Mhenni Benghorbal Nov 27 '12 at 4:14
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