1. Not finding help here? Sign up for a free 30min 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!

Help with a differential equation

  1. May 20, 2014 #1
    1. The problem statement, all variables and given/known data

    Hello

    I am new to this forum, but I hope I can get help with a problem I haven't been able to figure out what to do with.

    info:

    we have a one dimensional equation -d/dx [a(x) du/dx] = p(x)

    where we seek a solution u(x) where x is within [0,1] , that satisfies the 2 boundary conditions u(0) = 0, u(1) = 0

    p and a is given by a(x) = 1 and p(x) = 1

    any help with this problem would be very nice. On beforehand thanks


    2. Relevant equations



    3. The attempt at a solution

    My thought was to first find a general solution to the equation and then insert the conditions given. I have a hard time finding a general solution to the equation (-d/dx [a(x) du/dx] = p(x) ) so I feel a little stuck on how to approach it.
     
  2. jcsd
  3. May 20, 2014 #2
    Erm...just use this? I don't think it is possible to obtain a closed form expression for the general solution for arbitrary a(x) and p(x).
     
  4. May 20, 2014 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The general solution is very difficult- although I think it can be done in terms of
    [tex]u(x)= -\int_x^1\frac{1}{a(u)}\int_0^u p(t)dt du[/tex]

    But you are give that a(x)= 1 and p(x)= 1 so the problem is to solve [itex]\frac{d^2x}{dt^2}= -1[/itex] which can be done by two simple integrations.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Help with a differential equation
Loading...