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Finding the Integrating Factorby Happydog
Tags: integrating factor 
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#1
Jul1608, 07:46 PM

P: 3

Hi ok so te question is asking for me to fin the integrating factor of (y^{2}x+y)dy + (x^{2}y+2x)dy = 0 the only thing i know is that the integrating factor should be a function of xy
Can some one pleas explain how to do this? Thank you. 


#2
Jul1608, 09:47 PM

HW Helper
P: 2,616

You appear to have mistyped your problem. There 2 "dy"s here but no "dx".



#3
Jul1708, 05:03 AM

Math
Emeritus
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Thanks
PF Gold
P: 39,533




#4
Jul1708, 04:13 PM

P: 3

Finding the Integrating Factor
Yes the original equation is (y^{2}x+y)dx + (x^{2}y+2x)dy = 0, i have taken your sugestion but it did not work, i tryed a more general form of x^{n}y^{m} and multiplied it through to see if i could solve for the n and m and equate the two of them but the two are not equal i end up getting (m+2)=(n+2) and (m+1)=2(n+1).
so can any one also give me some advice on how to solve this problem i am having. Thank you. 


#5
Jul1808, 01:16 AM

HW Helper
P: 2,616

I think HallsofIvy's advice is spot on. Equate the two derivatives after differentiating the product of u and the expression preceding the dx and dy. Use the chain rule when differentiating u(xy) with respect to x and y only by denoting product xy as v. Simplify the resulting equation and you'll notice it reduces to a simple separable differential equation. Solve that and express u in terms of x,y only and you're done. I tried it out and it works like a charm.



#6
Jul1808, 04:48 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,533




#7
Jul1808, 09:11 AM

P: 3

Yeah it did work sorry about that, and as for havening it as x^{m}y^{n} other times you can use it to find out what power the x and y are to making it easer. mind you you have to know xy are the integrating factor.



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