X6n-2 = r X6n-1 = X6n = n-1 II ( i=0 n-1 PII i=0 n-1 9 II i=0 f3i-1P+f3ih (Jsip + f3i+1h) (£3i9 + £3i+1k f3i+19+f3i+2k f3i+1p+f3i+2h :) J3i+2P+ £34+3h) (13i-19-f31k f3i9-f3i+1k) faip + fai+1h) (fai+29 + fai+ak) f3i+19+f3i+2k) f3i+1p+f3i+2h)
X6n-2 = r X6n-1 = X6n = n-1 II ( i=0 n-1 PII i=0 n-1 9 II i=0 f3i-1P+f3ih (Jsip + f3i+1h) (£3i9 + £3i+1k f3i+19+f3i+2k f3i+1p+f3i+2h :) J3i+2P+ £34+3h) (13i-19-f31k f3i9-f3i+1k) faip + fai+1h) (fai+29 + fai+ak) f3i+19+f3i+2k) f3i+1p+f3i+2h)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Show me the determine yellow and all information is here
Transcribed Image Text:Bxn-10n-2
Xn+1 = axn-2 +
п 3 0, 1,...,
(1)
YXn-1+ dxn-4
1
Transcribed Image Text:The solution of the following special case of Eq.(1) has been obtained
Xn-1Xn-2
Xn+1 = Xn-2
(10)
Xn-1+ Xn-4
where the initial conditionsc –4, x-3, x-2, x–1, xo are arbitrary non zero real numbers.
Theorem 6. Let {xn}-4 be a solution of Eq.(10). Then for n = 0,1, 2, ...
n-1
( f3i+2P + f3i+3h`
II
f3i+3P+ f3i+4h,
f3iq + f3i+1k
f3i+1q + f3i+2k /
X6n+1
i=0
n-1
(f3i-2P + f3i-1h
hII
f3i-1p + f3ih
(f3i-19 + f3;k`
X6n-4
f3:9 + f3i+1k,
i=0
n-1
fsiP + fsi+1h (fsi-29 + fzi–1k`
kII
f3i+1P+ f3i+2h,
X6n-3
f3i-19 + fzik
i=0
n-1
fzi-1P+ f3ih
Faip+ fa+ih) \ Fsi+19 + fai+2k,
f3:4 + f3i+1k
П
X6n-2
%3D
i=0
п-1
(f3i+1p+ f3i+2h
PII
f3i+2p+ f3i+3h,
fai-19 – faik
f3iq – fai+1k,
X6n-1
i=0
fsip + fai+1h
f3i+1P+ f3i+2h ,
n-1
П
fai+19+ f3i+2k`
(f3i+29 + f3i+3k )
X6n
i=0
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