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Green's function for third order ODE

  1. Mar 2, 2012 #1
    I am trying to find a Green's function for a third order ODE.

    ([itex]\lambda[/itex] - d3/dx3 - [itex]\mu[/itex] d/dx)u = f(x) with boundary conditions u(0) = uxx(0) = ux(L) = 0 (L is finite).

    This has solution u(x) = c1em1x + c2em2x + c3em3x

    where m1, m2 and m3 are the roots of the characteristic equation from the ODE (they are not important at the moment).

    My question is how do I find the coefficients c1, c2 and c3?

    I know that it is going to be a 3 term piecewise function (as it is third order).

    Do I use the u(0) = uxx(0) = 0 BC's from 0 to s and u(0) = ux(L) = 0 from s to L?

    I need help on this please.
  2. jcsd
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