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Math Help - boundary value problem PDE

  1. #1
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    boundary value problem PDE

    Can someone help me find X(x) and Y(y) for u = XY in this PDE:

    ut = uxx - 2u
    boundary conditions: u(0,t) = 0, u(3,t) = 0
    initial condition: u(x,0) = 2sin(pi*x) - sin(4*pi*x)
    I know how to do the separation of variables, but again I'm having trouble finding X and Y.
    Thanks for your help.
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  2. #2
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    Quote Originally Posted by PvtBillPilgrim View Post
    Can someone help me find X(x) and Y(y) for u = XY in this PDE:

    ut = uxx - 2u
    boundary conditions: u(0,t) = 0, u(3,t) = 0
    initial condition: u(x,0) = 2sin(pi*x) - sin(4*pi*x)
    I know how to do the separation of variables, but again I'm having trouble finding X and Y.
    Thanks for your help.
    If you let u(x,t) = e^{-2t} v(x,t) then the PDE becomes

    v_t = v_{xx}

    with the same IC's and BC's.
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