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

Find the solution to [itex]y'=\frac{y+x}{y-x}[/itex] and graph the integral curves.

2. Relevant equations

Exact differential equation.

3. The attempt at a solution

I noticed it's an exact differential equation, I solved it implicitely. I reached that [itex]\frac{y^2 (x)}{2}-\frac{x^2}{2}-yx=\text{constant}[/itex]. I've looked into wikipedia about the integral curves but I don't really know how to find them here. If I understood well, an integral curve is a solution to the DE, so here it would be any y(x) that satisfies the DE. But here I can't get y(x) explicitely, so how do I graph y(x)?... Any idea is welcome!

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# Integral curves

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