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2nd order ODE

  1. Dec 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Solve:

    [tex]
    -D(x) \frac{d^2 T}{dx^2}=1
    [/tex]

    for [tex] x \in [0,1] [/tex]

    D(x) =10-3 in [0,0.5] and D(x) = 1 in (0.5,1]

    with homogeneous dirichlet boundary conditions

    3. The attempt at a solution
    So I have two quadratic equations with x(0)=x(1)=0 and continuity at x=0.5 but I'm missing a BC. I thought of the derative but I am uncertain. Can someone help me?
     
  2. jcsd
  3. Dec 26, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Missing a Boundary Condition? There are no boundary conditions given in the problem at all. You are asked for the general solution.

    Solve for the general solution. T1(x), of [itex]d^2T/dx^2= -1000[/itex] between 0 and 0.5. That answer will involve two unknown constants, say C and D. Then solve for the general solution, T2(x), of [itex]d^2T/dx^2= -1 between 0.5 and 1. That will involve two new constants, say E and F. Set the values of the functions and their first derivatives equal at 0.5 in order to write E and F in terms of A and B. You should then have a two "piece" definition for T(x) both involving the same two constants, A and B.
     
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