Find the power series in x for the general solution. (1 − x²)y" — 8xy' — 12y = 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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Question
can you help me solve this problem show your work how to find m, how to get the answer below.
Transcribed Image Text:5. an+2
a2m+3 =
(n+3)(n+4)
(n + 2)(n+1)
m + 2) (2m + 5)
(m + 1) (2m + 3)
∞
·an; a2m+2=
(m + 2) (2m + 3)
(m + 1)(2m + 1)
-a2m+1, so a2m+1
a1
Y
= ao Σ(m + 1)(2m +1)x²m +
m=0
-a2m, SO a2m = (m + 1) (2m + 1)ao;
(m + 1) (2m + 3)
3
-a₁. Thus,
Σ(m + 1) (2m+3)x²m+
m=0
Transcribed Image Text:5. Find the power series in x for the general solution.
(1 − x²)y" — 8xy' – 12y = 0
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