Answer
True
Work Step by Step
Let us take an example:
Suppose that $F(x)=xe^{ax}$
Now, $(D-a)^2[F(x)]=2$
We can see that $(D-a)^2$ annihilate $F(x)$.
Therefore, the given statement is $\bf{True}$.
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 - True-False Review - Page 524: c
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