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Given a linear differential operator L , the Green's function G(x, xi) solves

L G(x, xi) = δ(x− xi);

then to solve L y=f(x) we apply the operator ∫d xi , G(x, xi) to find y(x) . If L is a second order linear operator, then G is continuous in the first variable at x = xi and [G ^′ ] _xi− ^xi+=1 at x = xi .