(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve [tex]\frac{dy}{dx} = \frac{x-y}{x+y}[/tex]

2. Relevant equations

Homogeneous differential equation rules = [tex] v = \frac{y}{x} [/tex][tex] \frac{1}{y} = \frac{x}{y}[/tex] [tex] \frac{dy}{dx} = v + x\frac{dv}{dx}[/tex]

3. The attempt at a solution

[tex]\frac{dy}{dx} = \frac{x}{x+y}-\frac{y}{x+y} = \frac{1}{1+\frac{y}{x}} - \frac{1}{1+\frac{x}{y}}[/tex]

[tex]x+\frac{dv}{dx} = (1+v)^-1-(1+1/v)^-1 [/tex]

I'd like to know if what I've done here looks good so far? I'm not getting the right answer when I complete the integration, so I'm curious to know if I'm making an error after this point or if I've just completely set the problem up wrong. Thanks for any help!

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# Homework Help: Working the differential equation dy/dx = x-y/x+y

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