+0

# A fun calculus question

0
427
4
+227

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

#2
+26625
+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:

.

Alan  Jun 1, 2015
Sort:

#1
+85672
+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
+26625
+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:

.

Alan  Jun 1, 2015
#3
+85672
0

OK...thanks, Alan....

CPhill  Jun 1, 2015
#4
+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

### 10 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details