Question

(x^2+y^2)dx-2xydy=0

Answer 1

So it looks like you've got yourself and "exact" differential equation to solve. First off, how do you know if it's exact or not?

Well, the part on the left might be a partial wrt x and the right a partial wrt y. If so, we can simply solve this differential equation by noticing it falls into a nice little pattern of a function of x and y.

So we see if that's true by seeing if the partial wrt y of the left is equal to the partial wrt x of the right part, since they are already derivatives of "one function" then hopefully we can see that taking the other derivative will show the parts are equal, since it doesn't matter what order you take derivatives of an equation.

Answer 2

@Kainui Not really exact.

Answer 3

@primeralph Are you saying that d/dy(x^2+y^2)=/=d/dx(2xy)?

Answer 4

Negative sign.

Answer 5

Sure, maybe we can find an integrating factor that fixes it up though?

Answer 6

Yeah, that's the way to go.

Answer 7

@Kainui What happened?

Answer 8

Well, skinaq didn't ask any questions, I'm not going to be a blowhard for nothing, just to give some chump the answer.

Answer 9

The person seems new here.

Answer 10

@skinaq Do u want to differentiate it with respect to x??

Answer 11

yes @hesan