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
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 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa48641f7-73cd-4b4d-88d6-eed1a44c1144%2F5169f13a-7e82-49c8-98ab-2e667b4660de%2F9f1zu5p_processed.jpeg&w=3840&q=75)
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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