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### Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069

# find a differential operator that annihilates the given function.${{e}}^{-7x}$

$D+7$is the differential operator that annihilates the given function.

See the step by step solution

## Step 1: Differentiate the function continuously

Let the function be $f\left(x\right)={e}^{-7x}$

Then

$f\text{'}\left(x\right)=-7{e}^{-7x}=-7f\left(x\right)\phantom{\rule{0ex}{0ex}}⇒f\text{'}\left(x\right)+7f\left(x\right)=0$

Hence $\left(D+7\right)\left[f\right]=0$

Then $D+7$is the differential operator that annihilates the given function.