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[tex] y´´- a*y= \delta (x-d) [/tex]

with the boundary conditions:

[tex] \left.\frac{\partial y}{\partial x} \right|_ {x=0} = 0 [/tex]

[tex] lim _{x\rightarrow\infty} y = 0[/tex]

I get the homogeneous solution: [tex] y_H = C_1 exp (\sqrt{a}x) + C_2 exp (-\sqrt{a}x)[/tex]

and then to obtain the inhomogeneous solution (the particular solution), one should get the Green function. For these case, it is G equal to:

[tex] \{A exp (\sqrt{a}x) + B exp (-\sqrt{a}x)[/tex]

[tex] \{C exp (\sqrt{a}x) + D exp (-\sqrt{a}x)[/tex]

and the A, B, C, D coefficients should be obtain from the boundary conditions. This is my problem, I try to applied this boundary conditions but I have not idea how I can do it. Can someone help me?

Thanks