Question

how to solve d(xy) integrals?
for example d(xy)/(x^2+y^2)

Answer 1

is that real the question?

Answer 2

really*

Answer 3

you want to integrate d(xy)/(x^2+y^2)?

Answer 4

yes i was solivng diferential equation and got this

Answer 5

whats the differential equation ?

Answer 6

you take one variable as constant and integrate with respect to the other one

Answer 7

doesnt matter which one first, theyre interchangeable

Answer 8

are these partials ?

Answer 9

assuming d(xy)= dxdy

Answer 10

No.

Answer 11

dxy is definitely not dxdy
and about equation it will take a bit to find which 1 it was
but anyway is there any way to solve such an equation?

Answer 12

could you post the original differential equation ?

Answer 13

its an equation where i tried to pick an integral factor
(x+x^2+y^2)dy - ydx=0

and got that the factor is e^ (-2d(xy)/(xx+yy))

Answer 14

btw, you cannot take integral of an unknown function "y" with respect to another variable "x"

Answer 15

is that linear ?

Answer 16

nope. so integrating factor thing may not work right ?

Answer 17

well if u have 1d(xy) the answer is xy+c
so i guess there should be some way to solve harder integrals with dxy

Answer 18

theres task in book to find a factor for this equation

Answer 19

not sure how to proceed.. wolfram gives a simple solution
http://www.wolframalpha.com/input/?i=%28x%2Bx%5E2%2By%5E2%29dy+-+ydx%3D0

Answer 20

well anyway i was just wondering if such an integral is solvable and even real anywhere else

Answer 21

@eliassaab

Answer 22

ok thanks

Answer 23

@wio speaks this language of d(xy)'s and stuff.. . :)

Answer 24

what is \(\large \int \frac{d(y/x)} {1 + (y/x)^2}\) ?

Answer 25

um?

Answer 26

lol in which subject u get to do these crazy stuff ?

Answer 27

i dont think if you can connect mine integral to this 1
but this 1 should be arctan

the subject is differential equations

Answer 28

mhmm

Answer 29

\[
d(xy) = (xy)'dx = (y+xy')dx
\]

Answer 30

But that won't help you much because you'll have a rogue \(y\) term. So consider a transformation.

Answer 31

why is its (xy)'dx and not dy or whatever else? is it because y(x)?

Answer 32

I didn't say you couldn't do \[
d(xy) = (xy)'dy = (x'y+x)dy
\]

Answer 33

in this case \(x' = dx/dy\)

Answer 34

ohhh right

Answer 35

well thanks now i know how to deal with these integrals :D

Answer 36

I think you'll still have to use a transformation though.

Answer 37

yeah but the equation is of a lesser issue here as i just was wondering how to deal with these integrals because i have never had need to solve them

Answer 38

You mean actually doing the integral is less of a problem?

Answer 39

nope just in this case was looking for how to solve the integral

Answer 40

by the way is there any problem that we have also \[\frac{ 1 }{ x^2+y^2 }\] next to dxy