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Homework Help: Is this differential exact or not?

  1. Jun 29, 2008 #1
    1. The problem statement, all variables and given/known data
    Is the differential 3x^2y^3dx+3x^3y^2dy exact or not?
    Please show me how to do this problem using Euler's criterion.

    2. Relevant equations

    3. The attempt at a solution
    Euler says if partial deriv of first term = partial deriv of 2nd term then it must be exact right?
  2. jcsd
  3. Jun 29, 2008 #2


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    To be exact; the partial derivative with respect to y of the first term (the one proportional to dx) must be equal to the partial derivative with respect to x of the second term.
  4. Jun 29, 2008 #3


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    Yes it appears to be exact. Now all you need to do is to find the potential function.
  5. Jun 30, 2008 #4


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    Or, more mathematically, find the anti-derivative. "Potential function" is physics terminology.
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