solve this equation $z(z+y)dx+z(z+x)dy=0$

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I need to solve this following equation $$z(z+y)dx+z(z+x)dy=0$$

I get this from above equation

$$\frac{dx}{z(z+x)}+\frac{dy}{z(z+y)}=0$$

After there, I dont know what I need to do.

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If z is not a function of x or y, then you've already got the equation separated so you can simply integrate.

Paul Safier