Relation between Green's function and Particular integral

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Consider the differential equation,

$D_x f(x) =g(x)$ ,

The solution for this differential equation can be written using green's function as $ f(x)=\int G(x,x')g(x')dx' +\sum_{i=0}^n C_ih_{i} (x)$

such that $D_{x} h_{i}(x)=0$,

My question is can this "$ \int G(x,x')g(x')dx' +\sum_{i=0}^n C_ih_{i} (x)$" related to "Complementary function + Particular Integral " ?