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show that oC =0 ju n an Osdinasy point fos the equation Find He powes sesies vohttion tox tHe equation a bove

show that oC =0 ju n an Osdinasy point fos the equation Find He powes sesies vohttion tox tHe equation a bove

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.5: Trigonometric Graphs
Problem 64E
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show that an osdinasy point fox the equatron find tHe powes sesies vohetion tox tHe equation a bove
Transcribed Image Text:show that an osdinasy point fox the equatron find tHe powes sesies vohetion tox tHe equation a bove
Expert Solution
Step 1

Power series solution of a differential equation about an ordinary point:

Consider a second-order homogeneous linear differential equation of the form

P0xd2ydx2+P1xdydx+P2xy=0......(I)

where P0, P1, P2 are polynomials.

We assume throughout that P0, P1, P2 have no common factors. Then we say that x0 is an ordinary point of the equation if P0x0≠0

Then every solution of the equation (I) can be represented by a power series

y=∑n=0∞anx-x0n

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