I am trying to study green's function.suppose we have a differential equation,
$D_x f(x) =g(x)$ , We also provided with some boundary conditions for $f(x)$, But we supply this boundary conditions in green function for finding constants in green function, actually green function is the position representation of inverse of $D_x$ .
So my question is how is it possible to supply boundary conditions of $f(x)$ in $G(x,x')$ to find constants in $G(x,x')$.
Please give your precious little time to help me