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2- (a) Equating the coefficients of xk+r-1 to zero Σα. +r)(k +r - 1)ax xk+r-2 - [(k +r)(k +r- 1) + 2(k + r) - n(n + 1)]ak xk+r} = 0, k=0 yields to: ar+? =; a (b)Using the following recurrence relation 1 ak-2 - 1) ak = k (k - Show that the odd coefficients are (-1)' azn+1 = a1 n = 1,2,3, ... (? )!

2- (a) Equating the coefficients of xk+r-1 to zero Σα. +r)(k +r - 1)ax xk+r-2 - [(k +r)(k +r- 1) + 2(k + r) - n(n + 1)]ak xk+r} = 0, k=0 yields to: ar+? =; a (b)Using the following recurrence relation 1 ak-2 - 1) ak = k (k - Show that the odd coefficients are (-1)' azn+1 = a1 n = 1,2,3, ... (? )!

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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2- (a) Equating the coefficients of xk+r-1 to zero Σα- +r)(k +r- 1)ar x*+r-2 - [(k + r)(k +r- 1) + 2(k + r) – n(n + 1)]ax xk+r} = 0, k=0 yields to: ar+? =; ak-? %3D (b)Using the following recurrence relation 1 ak-2 k (k – 1) ak = Show that the odd coefficients are (-1)' a, ,n = 1,2,3, ... (?)! a2n+1 =
Transcribed Image Text:2- (a) Equating the coefficients of xk+r-1 to zero Σα- +r)(k +r- 1)ar x*+r-2 - [(k + r)(k +r- 1) + 2(k + r) – n(n + 1)]ax xk+r} = 0, k=0 yields to: ar+? =; ak-? %3D (b)Using the following recurrence relation 1 ak-2 k (k – 1) ak = Show that the odd coefficients are (-1)' a, ,n = 1,2,3, ... (?)! a2n+1 =
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