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

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

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 2{Ck + r)(k +r - 1)ak x**-2 - [(k +r)(k +r - 1) + 2(k +r) - n(n + 1)]a, x**r) = 0, yields to: ar42 =; ax-? ak- (b)Using the following recurrence relation 1 ak-2 k (k-1) ak = - Show that the odd coefficients are (-1) а, "п %3D 1,2,3, ... (?)! azn+1 =
Transcribed Image Text:2- (a) Equating the coefficients of x*+r-1 to zero 2{Ck + r)(k +r - 1)ak x**-2 - [(k +r)(k +r - 1) + 2(k +r) - n(n + 1)]a, x**r) = 0, yields to: ar42 =; ax-? ak- (b)Using the following recurrence relation 1 ak-2 k (k-1) ak = - Show that the odd coefficients are (-1) а, "п %3D 1,2,3, ... (?)! azn+1 =
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