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Homework Help: Help with a differential equation

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


    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.


    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


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    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.
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