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2- (a) Equating the coefficients of xk+r-1 > {(k +r)(k +r- 1)ag x**r-2 - [(k +r)(k+r-1) + 2(k+r)-n(n+ 1)]az x**r} = 0, k=0 yields to: ax+? = ak-? (b)Using the following recurrence relation 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 xk+r-1 > {(k +r)(k +r- 1)ag x**r-2 - [(k +r)(k+r-1) + 2(k+r)-n(n+ 1)]az x**r} = 0, k=0 yields to: ax+? = ak-? (b)Using the following recurrence relation 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 > {(k +r)(k+r- 1)ag x**r-2 - [(k +r)(k+r- 1) + 2(k+ r)- n(n + 1)Jag x*+r} = 0, k=0 yields to: ar4 =; ax-? %3D (b)Using the following recurrence relation 1 ak = - ak-2 k (k - 1) Show that the odd coefficients are (-1) а1 ,п%3D 1,2,3, ... (?)! azn+1 =
Transcribed Image Text:2- (a) Equating the coefficients of x*+r-1 to zero > {(k +r)(k+r- 1)ag x**r-2 - [(k +r)(k+r- 1) + 2(k+ r)- n(n + 1)Jag x*+r} = 0, k=0 yields to: ar4 =; ax-? %3D (b)Using the following recurrence relation 1 ak = - ak-2 k (k - 1) Show that the odd coefficients are (-1) а1 ,п%3D 1,2,3, ... (?)! azn+1 =
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