Theorem 3. Every solution of Eq.(1) is bounded if a + < 1.
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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Show me the steps of determine yellow and information is here step by step .(why)!!it complete

Transcribed Image Text:Bxn-10n-2
Xn+1 = axn-2+
п 3D 0, 1, ...,
(1)
YXn-1 + dxn-4

Transcribed Image Text:Theorem 3. Every solution of Eq.(1) is bounded if
a +
<1.
Proof: Let {n}-3 be a solution of Eq.(1). It follows from Eq.(1) that
(a+) -
BxnTn-2
Xn+1 = axn-2 +
< axn-2 +
Xn-2.
YXn + dxn-4
YXn
Then
Xn+1 < Xn-2
for all
n > 0.
Then the subsequences {x3n}0: {x3n+1}0; {X3n+2}0 are decreasing and so are
bounded from above by M = max{x_4, x_3, X–2, X –1, X0}.
n=0>
n=0
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