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Q16E

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Fundamentals Of Differential Equations And Boundary Value Problems

Found in: Page 337

Book edition 9th

Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages 616 pages

ISBN 9780321977069

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Short Answer

find a differential operator that annihilates the given function.
$x^{2} - e^{x}$

$D^{4} - D^{3}$ is the differential operator that annihilates the given function.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Differentiate the function continuously

Let the function be $f (x) = x^{2} - e^{x}$

Let $g (x) = x^{2}$

Then

$g' (x) = 2 x g'' (x) = 2 g''' (x) = 0 D^{3} [g] = 0$

Let $h (x) = - e^{x}$

Then

$h' (x) = - e^{x} h' (x) - h (x) = 0 (D - 1) [h] = 0$

Hence $D^{3} (D - 1) [f] = 0$

Then $D^{4} - D^{3}$ is the differential operator that annihilates the given function.

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