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Consider the differential equation y" + y + y = 0. Assuming that the solution can be written as a power series, y = ao + a1x + azx² + · … + a„r" + n=0 show that a, = 0 and that the other constants in this series must satisfy 1 2 an-2 . an Hence derive the power series for y(x) up to and including powers of x® assuming the constant ao = 1.

Consider the differential equation y" + y + y = 0. Assuming that the solution can be written as a power series, y = ao + a1x + azx² + · … + a„r" + n=0 show that a, = 0 and that the other constants in this series must satisfy 1 2 an-2 . an Hence derive the power series for y(x) up to and including powers of x® assuming the constant ao = 1.

Advanced Engineering Mathematics
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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Consider the differential equation y" + y + y = 0. Assuming that the solution can be written as a power series, y = ao + a1x + azx² + · … + a„r" + n=0 show that a, = 0 and that the other constants in this series must satisfy 1 2 an-2 . an Hence derive the power series for y(x) up to and including powers of x® assuming the constant ao = 1.
Transcribed Image Text:Consider the differential equation y" + y + y = 0. Assuming that the solution can be written as a power series, y = ao + a1x + azx² + · … + a„r" + n=0 show that a, = 0 and that the other constants in this series must satisfy 1 2 an-2 . an Hence derive the power series for y(x) up to and including powers of x® assuming the constant ao = 1.
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