Answer
False
Work Step by Step
We can see that $r=0$ is a thrice repeated root of auxiliary equation.
This implies that the trial solution is $y_p(x)=A_0x^3 +A_1 x^4+A_2 x^5+A_3 x^6+A_4 x^7$
Therefore, the given statement is $\bf{False}$.
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 525: g
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