Consider the differential equation
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:c)
Consider the differential equation
1
y" + y +y = 0.
Assuming that the solution can be written as a power series,
y = ao + a1x + a2x² + · · · + anx" + . ..=
anx"
n=0
show that a1 = 0 and that the other constants in this series must satisfy
1
an-2.
an
Hence derive the power series for y(x) up to and including powers of x6 assuming the
constant ao = 1.
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