Thread: greens functions

i am asked to find the greens function for

U' +kU=f(x)
with u(0)=0 and x>=0


i found the homogenous solution and used the 4 conditions...

my homogen soln was u=constant * exp(-kU)....

is it possible that my G(x,s)= 0 for x<s and X>s?

also how do i show that -u"= f(x) is not self adjoint with bc
u(0)=0 and u'(0) +u(1)=0

i have the greens function but the bc's dont hold for it?
is that right?

My understanding is if your equation is



then the Green's function is the solution to

.

So when you solve this equation you have in the first case



multiply by the integrating factor you have

,

and integrating



Enforcing the boundary condition and assuming we can deduce and therefore



Hope this helps. You might need to give more complete details to answer the second part.