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E36

[1SS]Given \(h=h(x)\), and \(πœƒβˆˆβ„\), solve the differential equations

\[ (D-πœƒ) f (x) = h (x) \]
\[ (D-πœƒ)^ 2 f (x) = h (x) \]
\[ (D^ 2+πœƒ^ 2) f (x) = h (x) \]
\[ (D^ 2-πœƒ^ 2) f (x) = h (x) \]

and special cases

\[ (D-1) f (x) = x^ k \]
\[ (D-πœƒ) f (x) = e^{𝛼 x} \]

(with \(π›Όβˆˆβ„‚\), and \(kβˆˆβ„•\), constants).

Solution 1

[1SV]

[ [1ST]]

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Authors: "Mennucci , Andrea C. G." .
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