I've been staring at this question for days and I've got to a point where I don't know where to go from...
The question asks
With the HLDE and the boundary conditions , find the two sided green's function.
I chosen the general solution to be . As it would satisfy the homogeneous HLDE. I know for the two sided green's function to be constructed, I need two functions that satisfy the homogeneous HLDE and satisfy the left and right boundary condition respectively.
Using the left hand side boundary condition,
Which means as and taking .
Using the right boundary condition and the values found above,
This is where my problem occurs. This shows that I have A & B equal to zero for the BVP, but this can't happen, as I won't be able to construct a green's function. Where have I gone wrong?
Thanks for your time.