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Homework Help: Exact DE question

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data
    determine whether the DE, (2x+y)dx-(x+6y)dy=0, is exact

    2. Relevant equations
    i understand how to determine if they are exact, I just don't understand this specific instance. for my case, M(x,y)=2x+y, but would N(x,y)=(x+6y), or (-x-6y)?

    3. The attempt at a solution
    using my first N(x,y), the equation is exact, however, using the second, they are not exact.

    Just need clarification at this point
    Last edited: Dec 11, 2011
  2. jcsd
  3. Dec 11, 2011 #2

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    Hi Eastonc2! :smile:

    Your N(x,y)=(-x-6y).
    That is how it matches the definition of an exact DE.

    But how did you determine that it was exact with the first N(x,y)?
    Because I don't think it is.
  4. Dec 11, 2011 #3
    ah, my fault, M(x,y)=2x+y

    i was looking at the equation above it for that first part. the second part is correct though.
  5. Dec 11, 2011 #4

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    Ah, now I see your dilemma.

    To make sure, perhaps you should try to find a function of which the partial derivatives match with M(x,y) and N(x,y).
    Can you find such a function?
  6. Dec 11, 2011 #5


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    Have you studied the case where M and N are homogeneous of the same degree, as these are?
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