Consider the following differential equation: (x² + 1)y″+8xy′+7y = 0. Suppose that this equation has a series solution of the form: y = Σ (x Σαn (2 - 7)" n=0 on some open interval that contains the point x0 = 7. Determine the singular points z in the complex plane. Enter the solutions as a comma-separated list. z = Making an appropriate sketch that shows the geometry of the problem, find the minimum radius of convergence p as the distance from the expansion point to the nearest singular point in the complex plane. Note: if the answer is a radical that can be reduced, make sure to simplify your answer. P= Find the minimum interval of convergence, I = (xop, xo+p). I =
Consider the following differential equation: (x² + 1)y″+8xy′+7y = 0. Suppose that this equation has a series solution of the form: y = Σ (x Σαn (2 - 7)" n=0 on some open interval that contains the point x0 = 7. Determine the singular points z in the complex plane. Enter the solutions as a comma-separated list. z = Making an appropriate sketch that shows the geometry of the problem, find the minimum radius of convergence p as the distance from the expansion point to the nearest singular point in the complex plane. Note: if the answer is a radical that can be reduced, make sure to simplify your answer. P= Find the minimum interval of convergence, I = (xop, xo+p). I =
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:Consider the following differential equation:
(x² + 1)y″+8xy′+7y = 0.
Suppose that this equation has a series solution of the
form:
y =
Σ
(x
Σαn (2 - 7)"
n=0
on some open interval that contains the point x0 = 7.
Determine the singular points z in the complex plane. Enter
the solutions as a comma-separated list.
z =
Making an appropriate sketch that shows the geometry of
the problem, find the minimum radius of convergence p as
the distance from the expansion point to the nearest
singular point in the complex plane. Note: if the answer is a
radical that can be reduced, make sure to simplify your
answer.
P=
Find the minimum interval of convergence,
I = (xop, xo+p).
I =
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