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: Have I answered these questions on Laplace's equation correctly?

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    I missed the lecture on this so I just wanted to check if I am doing this correctly?

    Which of the following functions obey Laplace’s equation?
    a) Ψ(x, y) = 2xy
    b) Ψ(x, y) = x^3 - 3y^2
    c) Ψ(x, y) = x^4 - 6x^2.y^2
    d) Ψ(x, y) = e^x.siny
    e) Ψ(x, y) = sinxsinhy

    2. Relevant equations

    [tex]\nabla[/tex][tex]^{2}[/tex] = [tex]\partial^2/\partial x^2 + \partial^2/\partial y^2 + \partial^2/\partial z^2[/tex]

    3. The attempt at a solution

    I am not showing me working out the partial derivatives of each question so I'm just showing the final line of my working.

    a) 0 - 0 = 0 so yes

    b) 6x - 6x = 0 so yes

    c)12x^2 - 12y^2 - 12x^2 so no it doesn't

    d) e^x.sin(y) - e^x.sin(y) = 0 so yes

    e) -sin(x)sinh(y) + sin(x)sinh(y) = 0 so yes
  2. jcsd
  3. Oct 16, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi lozzyjay! :smile:

    ok except for:
  4. Oct 16, 2008 #3
    Ah yes! Thank you! :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook