Prove that any solution of the equation 1 + x = 0, t> 2 has a zero on the interval [2īn, 27(n + 1)] for any n E N. Hint. Apply the second Sturm comparison theorem when comparing to the oscillatory equation x" +x = 0, where 1 + > 1, 1 – < 1 on the interval [2an, 27(n + 1)] for any n E N.
Prove that any solution of the equation 1 + x = 0, t> 2 has a zero on the interval [2īn, 27(n + 1)] for any n E N. Hint. Apply the second Sturm comparison theorem when comparing to the oscillatory equation x" +x = 0, where 1 + > 1, 1 – < 1 on the interval [2an, 27(n + 1)] for any n E N.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Prove that any solution of the equation
1+
x = 0, t > 2 has
a zero on the interval [27n, 27 (n + 1)] for any n E N.
Hint. Apply the second Sturm comparison theorem when comparing to the oscillatory
equation x" +x =
0, where 1+> 1, 1 – < 1 on the interval [27n, 27(n + 1)] for
any n E N.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf188ab9-8d84-46fe-8000-5fae5eb508b3%2Fb60a2703-1aef-4d18-bf77-d9fa5d4100d6%2Fychidpd_processed.png&w=3840&q=75)
Transcribed Image Text:Prove that any solution of the equation
1+
x = 0, t > 2 has
a zero on the interval [27n, 27 (n + 1)] for any n E N.
Hint. Apply the second Sturm comparison theorem when comparing to the oscillatory
equation x" +x =
0, where 1+> 1, 1 – < 1 on the interval [27n, 27(n + 1)] for
any n E N.
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