Green's function for third order ODE

1. Mar 2, 2012

squenshl

I am trying to find a Green's function for a third order ODE.

($\lambda$ - d3/dx3 - $\mu$ 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.
Cheers.