1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor

    This is a separable equation.
    dg/g= ydy

    Integrate both sides.

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


    User Avatar
    Science Advisor

    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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook