Consider the ODE
y''(x) − y(x) = f(x), lim x→±∞
y(x) = 0
for some sufficiently smooth function f. Your task in this problem is to solve the ODE via Green’s Function.
(a) Setup the corresponding Green’s Function problem in terms of the Delta function.
(b) Determine the Green’s function G(x, xs).
(c) Determine the solution of the ODE in terms of the Green’s function you found.
This should get you started.
web.iisermohali.ac.in/Faculty/anoshjoseph/courses/2019_odd_mmp1/lec29.pdf