Homework Help: Integral curves

1. Jan 30, 2012

fluidistic

1. The problem statement, all variables and given/known data
Find the solution to $y'=\frac{y+x}{y-x}$ 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 $\frac{y^2 (x)}{2}-\frac{x^2}{2}-yx=\text{constant}$. 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!

2. Jan 30, 2012

HallsofIvy

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

3. Jan 30, 2012

fluidistic

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.