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General formula for causal Green's function of linear differential operatorof given degree in one variable is given according to coefficient functions ofdifferential operator as a series of integrals. The solution also providesanalytic formula for fundamental solutions of corresponding homogenous lineardifferential equation as series of integrals. Furthermore, multiplicativeproperty of causal Green's functions is shown and by which explicit formulasfor causal Green's functions of some classes of decomposable lineardifferential operators are given. A method to find Green's function of generallinear differential operator of given degree in one variable with arbitraryboundary condition according to coefficient functions of differential operatoris demonstrated.

Green's Function For Linear Differential Operators In One Variable