Hey guys,

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.