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:
Now, naturally, I was interested in finding the original equation, but it gave me problems, mainly this:
I have no clue what tto do with this, seeing as all the integration techniques I know are useless. Help, please!
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 + C1
(And C1 is just a constant )
y^2 = 2C1 - x^2 let 2C1 = C2
y = ±√[C2 - x^2)
I believe this might be correct......Alan....will you check it????
I think it's more complicated than this Chris. Your result can be written as x2 + y2 = constant.
This gives 2x + 2ydy/dx = 0 or dy/dx = -x/y.
Here's my attempt: