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January 16th, 2014, 04:56 PM   #1
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Inexact differential

how do you solve this inexact differential. dz=xdx+(x+2y)dy. I get e^(y/x) as the integrating factor. Is it correct? help would be appreciated!
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January 17th, 2014, 04:51 AM   #2
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Re: Inexact differential

Well, if is an integrating factor then would be an "exact" differential, meaning that there is some function, F, of x and y, such that which would mean that and . That would mean that the two mixed second derivatives and must be equal. But they are not so that is NOT an exact differential so is NOT an integrating factor.

However, I don't know what you mean by "solve " or even by " itself! Because is not an exact differential, there is NO function, z, such that dz is equal to it. So what is the problem you are trying to solve, really? If it were that would make sense because you could multiply by the integrating factor on both sides and the right side would still be 0.
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January 17th, 2014, 06:39 AM   #3
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Re: Inexact differential

Quote:
Originally Posted by HallsofIvy
Well, if is an integrating factor then would be an "exact" differential, meaning that there is some function, F, of x and y, such that which would mean that and . That would mean that the two mixed second derivatives and must be equal. But they are not so that is NOT an exact differential so is NOT an integrating factor.

However, I don't know what you mean by "solve " or even by " itself! Because is not an exact differential, there is NO function, z, such that dz is equal to it. So what is the problem you are trying to solve, really? If it were that would make sense because you could multiply by the integrating factor on both sides and the right side would still be 0.
thanks your your reply. so, whats the integrating factor for xdx+ (x+ 2y)dy= 0?
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