(1+x²)y" + 10xy' + 20y = 0
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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show the correct solution for the secod item.
![Find the G.S. about x, = 0 for the following DE's
1.
(x² + 4)y" + 2xy' – 12y = 0
(-1)*(k + 1)3a,x 2k
2k (2k – 3)(2k – 1)
5
Answer: y = a, + a,x +za;x³ +
k=1
2.
(1 + x²)y" + 10xy' + 20y = 0
(-1)*(2k + 1)(2k + 3)(k + 1)a,x²k -
3
(-1)*(k + 1)(k + 2)(2k + 3)a,x2k+1
Answer: y = a, + a,x +
k=1
k=1
3.
(x² + 4)y" + xy = x + 2
1
1- ao
Answer: y = > anx" = a, + a,x +7x² +
2 - ao
x5 + ·
320
...
24
48
n=0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc5bda4f-1b26-40fa-9642-8174f23c93ac%2F7069b34a-3374-48b3-97b2-e36b4c964892%2F6ei7gm8_processed.png&w=3840&q=75)
Transcribed Image Text:Find the G.S. about x, = 0 for the following DE's
1.
(x² + 4)y" + 2xy' – 12y = 0
(-1)*(k + 1)3a,x 2k
2k (2k – 3)(2k – 1)
5
Answer: y = a, + a,x +za;x³ +
k=1
2.
(1 + x²)y" + 10xy' + 20y = 0
(-1)*(2k + 1)(2k + 3)(k + 1)a,x²k -
3
(-1)*(k + 1)(k + 2)(2k + 3)a,x2k+1
Answer: y = a, + a,x +
k=1
k=1
3.
(x² + 4)y" + xy = x + 2
1
1- ao
Answer: y = > anx" = a, + a,x +7x² +
2 - ao
x5 + ·
320
...
24
48
n=0
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