I'm back! Maybe..... Anywho, here's my problem:

So, I was messing around with slope fields and got this pretty cool field given by the following equation:

$$\frac{dy}{dx}=\frac{x+y}{x-y}$$

Now, naturally, I was interested in finding the original equation, but it gave me problems, mainly this:

$$\int_{}^{}xdy$$

I have no clue what tto do with this, seeing as all the integration techniques I know are useless. Help, please!

ThisGuy
May 31, 2015

#1**+5 **

Cross-multiply .......this gives........

(x - y) dy = (x + y) dx integrate both sides

∫ ( x- y) dy = ∫ (x + y) dx

[On the left side, x is considered to be a constant......same with y on the right side]

xy - y^2/2 = x^2/2 + xy + C subtract xy from each side

-y^2/2 = x^2/2 + C_{1 }

(And C1 is just a constant )

y^2 = 2C_{1} - x^2 let 2C_{1} = C_{2}

y = ±√[C_{2} - x^2)

I believe this might be correct......Alan....will you check it????

CPhill
May 31, 2015