Answer
True
Work Step by Step
Since, $y^{\prime\prime}+9y=\cos (3x)$
The roots of the auxiliary equation are: $3i,-3i$
So, the correct trial solution must be:
$y_p=A_0xe^{3ix}+B_0e^{4ix}$
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 - 8.4 Complex-Valued Trial Solutions - True-False Review - Page 528: f
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