Answer
$F(x)=4G(x)$
Therefore, $D^2+4r+5$ is the annihilator of $F(x)$.
Work Step by Step
We are given that $D^2+4r+5$ is the annihilator of $G(x)= e^{-2x} \sin x$
So, $F(x)=4G(x)$
Therefore, $D^2+4r+5$ is the annihilator of $F(x)$.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 8 - Linear Differential Equations of Order n - 8.3 The Method of Undetermined Coefficients: Annihilators - Problems - Page 525: 5
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