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

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

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 x*+r-1 to zero > {(k +r)(k + r- 1)ar xk+r-2 - [(k +r)(k +r - 1) + 2(k +r) – n(n + 1)]ag xk+r} = 0, k=0 yields to: ak+? = 7 ak-? (b)Using the following recurrence relation 1 ar = ak-2 k (k – 1) Show that the odd coefficients are (-1)? а1 ,п %3D 1,2,3, ... a2n+1 = (?)!
Transcribed Image Text:2- (a) Equating the coefficients of x*+r-1 to zero > {(k +r)(k + r- 1)ar xk+r-2 - [(k +r)(k +r - 1) + 2(k +r) – n(n + 1)]ag xk+r} = 0, k=0 yields to: ak+? = 7 ak-? (b)Using the following recurrence relation 1 ar = ak-2 k (k – 1) Show that the odd coefficients are (-1)? а1 ,п %3D 1,2,3, ... a2n+1 = (?)!
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