Using fourier/laplace transform and green's function

1. Aug 1, 2008

captain

i am having trouble distinguishing when to use fourier or laplace transform to solve any linear differential equation (it can be an ODE or PDE). What are the advantages and disadvantages of using each? Also for a green's function (take it to be a function of x, x') when solving for it, is it true that for an ODE you take a case when x>x' and x<x' so that you get two homogenous equations when the dirac delta function equals 0 and for the PDE you use fourier transform? Can you used a laplace transform to evaluate a greens function (although i haven't seen it done in any text i have read)? sorry about all these questions but i feel confused. thx in advance to whoever answers some or all these questions.