Solving Exact Diff. Eq: Finding Integral Curves

[fluidistic]

Homework Statement

Find the solution to $y'=\frac{y+x}{y-x}$ and graph the integral curves.

Homework Equations

Exact differential equation.

The Attempt at a Solution

I noticed it's an exact differential equation, I solved it implicitely. I reached that $\frac{y^2 (x)}{2}-\frac{x^2}{2}-yx=\text{constant}$. 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!

 

[HallsofIvy]

Choose a number of specific values for the constant and graph those curves.

 

[fluidistic]

Choose a number of specific values for the constant and graph those curves.

Ah I see, thank you very much. I graph point per point, maybe I'm missing an obvious curve or something.
I take C=1. I set x=0 and I get $y=\pm \sqrt 2$. I graph this in the x-y plane. Now I set x=2 and I get a quadratic equation for y, which yields $y= 2 \pm \sqrt {10}$. So for a fixed C, there are 2 curves; maybe parabolas or hyperbolas.