Find a power series expansion about x = 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. (x² +1) y" - xy' + y =0 What is the power series solution to the differential equation? 22). Ο A. _y(x)=ao | Σ n=1 (-1)+1(1.3.5|2n-3) (2n)(2n-1)(2.4.6.-(2n-2))" ∞0 OB. y(x) = a 1+ X n = 0 ∞0 OC. y(x) =a -1+ Σ n=0 OD. y(x)=ao 1+ Σ n=1 x²n (-1)^ (1.3.5|2n-1) (2n+2)(2n+ 1)(2.4.6...(2n))^ (-1) (1 3.5 2n-11) (2n + 1)(2.4.6...(2n)) -x²n -x2n + a₁x (-1)+1(1.3.5|2n-3) (2n) (2n-1)(2 4.6...(2n-2))^ + a₁x + a₁x 2012 - 2,² a₁x
Find a power series expansion about x = 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. (x² +1) y" - xy' + y =0 What is the power series solution to the differential equation? 22). Ο A. _y(x)=ao | Σ n=1 (-1)+1(1.3.5|2n-3) (2n)(2n-1)(2.4.6.-(2n-2))" ∞0 OB. y(x) = a 1+ X n = 0 ∞0 OC. y(x) =a -1+ Σ n=0 OD. y(x)=ao 1+ Σ n=1 x²n (-1)^ (1.3.5|2n-1) (2n+2)(2n+ 1)(2.4.6...(2n))^ (-1) (1 3.5 2n-11) (2n + 1)(2.4.6...(2n)) -x²n -x2n + a₁x (-1)+1(1.3.5|2n-3) (2n) (2n-1)(2 4.6...(2n-2))^ + a₁x + a₁x 2012 - 2,² a₁x
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:Find a power series expansion about x = 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients.
(x²+1) y' - xy' + y = 0
What is the power series solution to the differential equation?
O
∞
A. _y(x)=ao| Σ
n=1
O B. y(x) = a1 +
(-1)+1(1.3.5|2n-31)
∞
Σ
n = 0
(2n)(2n-1)(2 4.6.(2n-2))
(-1) (1.3.5... |2n-1)
(2n + 2)(2n +1)(2• 4 • 6…. (2n))
OC. y(x) =a -1+ Σ
n=0
∞
O D. y(x) = a 1 + Σ
n=1
●
2n
X
5...
(-1) (1.3-5--|2n-11)
(2n+ 1)(2.4.6...(2n))
+ a₁x
2n
"X²
-x²n
(-1)+1(1.3.5... |2n-3)
(2n) (2n-1)(2 4.6.(2n - 2))´
x²n
+ a₁)
X
+ a₁x
+ a₁x
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