The point x = 0 is a regular singular point of the given differential equation. Find the recursive relation for the series solution of the DE below. Show the substitution and all the steps to obtain the recursive relation. Do not solve the equation for y=y(x) xy" + 4y' - xy = 0, a. Ck+1= b. Ck+1= c. Ck d. Ck= e. Ck= O O a O C e 1 (k+r+ 1)(k+r+3) 1 (k+r+ 1)(k+r+4) -Ck-1, k≥1 1 k+r k+r ·Ck-1, k≥1 -Ck-1, k>1 -Ck-1, k≥1 (k+r)² +5(k+r) 1 (k+r)²-2(k+r)-8 ·CK-2, k≥2
The point x = 0 is a regular singular point of the given differential equation. Find the recursive relation for the series solution of the DE below. Show the substitution and all the steps to obtain the recursive relation. Do not solve the equation for y=y(x) xy" + 4y' - xy = 0, a. Ck+1= b. Ck+1= c. Ck d. Ck= e. Ck= O O a O C e 1 (k+r+ 1)(k+r+3) 1 (k+r+ 1)(k+r+4) -Ck-1, k≥1 1 k+r k+r ·Ck-1, k≥1 -Ck-1, k>1 -Ck-1, k≥1 (k+r)² +5(k+r) 1 (k+r)²-2(k+r)-8 ·CK-2, k≥2
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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Transcribed Image Text:The point x = O is a regular singular point of the given differential equation. Find
the recursive relation for the series solution of the DE below. Show the
substitution and all the steps to obtain the recursive relation. Do not solve the
equation for y=y(x)
xy" + 4y' - xy = 0,
1
a. Ck+1=
(k+r+ 1)(k+r+3)
1
b. Ck+1 = (k+r+1)(k+r+4)
·Ck-1, k≥ 1
с. Ск
d. Ck²
e. Ck
O
a
P
=
e
11
||
1
k+r
I
k+r
·Ck-1, k≥1
-Ck-1, k≥1
-Ck-1, k≥1
(k+r)² +5(k+r)
1
(k+r)²-2(k+r) -8
·CK-2, k≥2
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