Given the following differential equation 2 y' + x2 y = 0 Plug in the appropriate power series for "y" and "y'" in order to convert the differential equation into a power series. Σ 00 00 Α ΣηA, xb - ) n = 1 2 A x" + = 0 n = 0 00 2 2n A x(m - 1) + ΣΑx+ ) B = 0 n = 1 n = 0 Σ 00 2 2n A x(n - 1) 2 x2 A x" = o n = 1 n = 0 E 2n A, x(n - 1) + E A, = 0 n = 1 n = 0 00 E [3n A + 1) = 0 n = 1
Given the following differential equation 2 y' + x2 y = 0 Plug in the appropriate power series for "y" and "y'" in order to convert the differential equation into a power series. Σ 00 00 Α ΣηA, xb - ) n = 1 2 A x" + = 0 n = 0 00 2 2n A x(m - 1) + ΣΑx+ ) B = 0 n = 1 n = 0 Σ 00 2 2n A x(n - 1) 2 x2 A x" = o n = 1 n = 0 E 2n A, x(n - 1) + E A, = 0 n = 1 n = 0 00 E [3n A + 1) = 0 n = 1
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
q16
Transcribed Image Text:Given the following differential equation
2 y' + x2 y = 0
Plug in the appropriate power series for "y" and "y'" in order to convert the differential equation into a power series.
Σ
00
Σ
00
A 2 n A x(" - 1)
2 A x"
+
= 0
n = 1
n = 0
00
00
2 2n A x(m - 1)
n = 1
B
A x(n
+ 2)
+
= 0
n = 0
2 2n A x(m - 1)
Σ
2 x2 A x" = 0
n = 1
n = 0
00
E 2n A, x(u - 1) + E A,
= 0
n = 1
n = 0
00
E 3n A
+ 1) = 0
n = 1
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