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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

Best Answer 

 #2
avatar+26329 
+10

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:

 integration: 

.

Alan  Jun 1, 2015
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4+0 Answers

 #1
avatar+78719 
+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 + 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????

 

 

 

CPhill  May 31, 2015
 #2
avatar+26329 
+10
Best Answer

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:

 integration: 

.

Alan  Jun 1, 2015
 #3
avatar+78719 
0

OK...thanks, Alan....

 

 

CPhill  Jun 1, 2015
 #4
avatar+227 
+5

Whoah... Okay, thanks... That was really involved, but I should've assumed it would be! Thanks for the help!

ThisGuy  Jun 1, 2015

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