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Green's function for BVP

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Obtain the Green's function for BVP (and use it to express the solution for the given data):

    -y''(x) = f(x), 0 < x < 1, y'(0) = a, y(1) = b

    2. Relevant equations

    3. The attempt at a solution

    I have found 2 solutions to the homogeneous equation
    y1(x) = ax, satisfies y'(0) = a
    y2(x) = x - 1 + b, satisfies y(1) = b

    Then I need to consider a general solution y(x) = c1(x)y1(x) + c2(x)y2(x)
    So y' = c1y1' + c2y2' (imposing c1'y1 + c2'y2 = 0)
    y'' = c1y1'' + c2y2'' + c1'y1' + c2'y2'

    So to satisfy the boundary conditions I need
    a = ac1(0) + c2(0)
    b = ac1(1) + bc2(a)

    I am not sure how to impose these into the integrals for c1 and c2 (as I would in the case when I have something like y(a) = 0 = y(b)?
  2. jcsd
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