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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.2012-11-25
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    Thanks for your reply. It may be just a case of trial and error.2012-11-25
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    See my solution for your [other problem](http://math.stackexchange.com/questions/245217/partial-differential-with-integrating-factor).2012-11-27

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