Question

(y^2+2xy)dx-x^2dy=0
special integrating factors

Answer 1

integrating factor is 2y/x^2 but do i integrate it all or just 1/x^2?

Answer 2

integrate as it is written

so for the first term you get
xy^2+yx^2+c(y)

and the second is
yx^2+d(x)

Answer 3

idk what you did there

Answer 4

e^int(2y/x^2)=?

Answer 5

whats int?

Answer 6

integral

Answer 7

what is the integrand

Answer 8

(2y/x^2)

Answer 9

what are integrating with respect to.

Answer 10

dy? dx?

Answer 11

dx

Answer 12

so we would just integrate 1/x^2? right? since its dx

Answer 13

yes

Answer 14

that's what i thought

Answer 15

but if you don't know your limits of integration, theres a constant c(y)

Answer 16

yeah from the indefinite integral

Answer 17

yes

Answer 18

so integration factor is x^2 and left side gives us
\[(x^2y^2+2x^3y)dx-x^4dy=0\]

Answer 19

no left side but multiplying IF through equation

Answer 20

I think you need to check your integration again.

Answer 21

i tried multiplying the x^2 through and it didn't give me exact so i don't think that is right....oh it should be x^3/3 shouldn't it :/

Answer 22

I integrated it in my first post. And you can't multiple terms by another function within the integral.

Answer 23

or just x cause its x^-2 so integral of that -1/x

Answer 24

I'm not sure where you got that from.

Answer 25

our integration factor is 2y/x^2. taking integral of that with respect to x

Answer 26

i need the right integration factor to multiply through the equation to make it exact

Answer 27

you can't multiply by x or y, only constants.

Answer 28

taking 10 if anyone comes to help....be back soon