Question

Hi everyone! I'm doing an exact DE and P(x)=(1+2/y)...Can anyone explain why the domain is 0 11 years ago

Answer 1

@ganeshie8 @Kainui

Answer 2

I am under the impression by my book that you can determine the domain by just analyzing P(x)...is this true? Or am I missing something?

Answer 3

are you given initial conditions ?

Answer 4

no

Answer 5

because your function would contain ln i believe

Answer 6

Maybe I should have stated that P(x) isn't the whole problem of course, it's just the P(x) part of the standard form dy/dx + P(x)y=f(x)

Answer 7

;)

Answer 8

hmm...

Answer 9

let me think about that for a sec or 2...

Answer 10

ok what exact formula u are leaning ?

Answer 11

see if this helps
http://apcentral.collegeboard.com/apc/members/repository/ap07_calculus_DE_domain_fin.pdf

Answer 12

not sure what you mean ikram...I'm just referring to solving exact differential equations...not sure I understand your question

Answer 13

lemme look Ganeshie brb

Answer 14

That's alot to go over Ganeshie...I just don't have the time, I have an exam on Wednesday and not knowing this will hardly impact my score...I was hoping for a simple answer so i can go back to studying?

Answer 15

@hartnn @phi

Answer 16

P(x) can't be equal to 1 + 2/y as it should be a function of x?

Answer 17

yes, P(x) = (1+2/y) this is just to find the integrating factor so it's fine...I just need to know about the domain is all

Answer 18

it may have been P(y)...doesn't matter for what I need to know though...just the domain part

Answer 19

The integrating factor uses P(x) which is normally a function of x not y.
What's the complete problem?

Answer 20

this problem was flipped...sorry...it is P(y)-(1+2/y)
so I just needed to know why the domain was 0<y<infinity

ydx + (xy + 2x _ye^y)dy = 0

Answer 21

P(y)=(1+2/y)

Answer 22

it looks like f(y) also plays a factor in deciding the domain...thus both P(y) and f(y) must be defined on the same interval...thanks for the help everyone...I'm closing this one down