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