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Partial Differentiation HELP!

  1. Dec 13, 2009 #1
    1. The problem statement, all variables and given/known data
    http://img94.imageshack.us/img94/3853/physicse.jpg [Broken]

    3. The attempt at a solution
    I kept y fixed, and so I ended up with the following equation:

    Integ[dU/U] = Integ[x]

    And we end up with: U(x,y) = e^x * g(y)

    To solve g(y), we sub the solution into the 2nd PDE provided to give:

    d/dy[e^x * g(y)] = y[e^x * g(y)]

    Dividing through by e^x: d/dy [g(y)] = y*g(y)

    I was stuck at this point, so took a peek at the answers to find the lecturer wrote:
    => ln[g(y)] = 1/2*y^2 + c

    How did he come to that? I can't solve this equation, could someone please help me out?

    Thank you very much!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Dec 13, 2009 #2
    I have also tried working the other way round but still, no joy.

    Any help?
     
  4. Dec 14, 2009 #3
    I don't think that is quite the right answer,

    Cause couldn't for the first step anything like g(y)e^x + h(y) work?

    So pluging that into the second equation you get g'(y)e^x+h'(y) = y(g(y)e^x+0)
    so h'(y)= c, and g'(y)=yg(y), you can solve from there.
     
  5. Dec 14, 2009 #4

    HallsofIvy

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    This is a separable equation.
    dg/g= ydy

    Integrate both sides.

     
    Last edited by a moderator: May 4, 2017
  6. Dec 14, 2009 #5

    HallsofIvy

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    No, it wouldn't. The derivative of that, with respect to x, is g(y)e^x, NOT U(x,y)= g(y)e^x+ h(y). What Lavace did was correct.

     
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