Answer
False
Work Step by Step
Polynomial is: $r(r-1)-5r-7=0 \\ r^2-6r-7=0 \implies (r-7)(r+1)=0\\ r=-1, 7$
But, $x^{7}$ and $x^{-1}$ are not oscillatory.
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 - 8.8 A Differential Equation with Nonconstant Coefficients - True-False Review - Page 567: f
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