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Exact differential

  1. Sep 9, 2010 #1
    1. The problem statement, all variables and given/known data

    x(dy/dx) = 2xe^x - y + 6x^2

    2. Relevant equations

    3. The attempt at a solution

    I am trying to show this is an exact differential (book has an answer, it must be )

    I rearranged the problem to be :

    2xe^x - y + 6x^2 dx = x dy

    Partial derivatives (using & for that symbol that represents partial)
    &m/&y = -1
    &m/&x = 1

    -1 doesn't equal 1

    Any idea where my mistake is?
  2. jcsd
  3. Sep 9, 2010 #2


    Staff: Mentor

    Write the equation as Mdx + Ndy = 0, and you'll see that this equation is exact, since My = Nx.
  4. Sep 9, 2010 #3
    *face palm*

    Thank you lol :P

    That would flip the sign of y and make it 1=1.
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