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Fundamentals Of Differential Equations And Boundary Value Problems

R. Kent Nagle, Edward B. Saff, Arthur David Snider

$Math Studyset Vaia Explanations$ Math

9th Edition · 616 pages

ISBN: 9780321977069

Chapter 6: Q11E (page 337)

. find a differential operator that annihilates the given function.
$x^{4} - x^{2} + 11$

Short Answer

Expert verified

$D^{5}$ is the differential operator that annihilates the given function.

Step by step solution

Differentiate the function continuously

Let the function be $f (x) = x^{4} - x^{2} + 11$

Then

$f' (x) = 4 x^{3} - 2 x f'' (x) = 12 x^{2} - 2 f''' (x) = 24 x f^{(4)} (x) = 24 f^{(5)} (x) = 0$

Hence $D^{5} [f] = 0$

Then $D^{5}$ is the differential operator that annihilates the given function.

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. find a differential operator that annihilates the given function.x4-x2+11

Short Answer

Step by step solution

Differentiate the function continuously

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Most popular questions from this chapter

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. find a differential operator that annihilates the given function.
$x^{4} - x^{2} + 11$