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The Non-Homogeneous Differential Equation

$$Ly=R$$ Where $$ L=F(D)= \sum_i a_iD^i $$

Is solved with the way below.

$$ Ly=R \Rightarrow y=\frac{R}{L}=\frac{R}{F(D)}$$

Then we expand the qiotient $ \frac{1}{F(D)}$ into Taylor Series in the neighborhood of 0 (McLaurin).

In order to expand F(D) we have to give $D=\frac{d}{dx} $ a value. How can we give a differential operator a value?

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    See Laplace transform where $D$ gets replaced by the "frequency" variable $s$. – 2017-01-06

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