Consider the differential equation (x² – 2x + 1)y" + xy' – y = 0 a) Show xo = -1 is an ordinary point of the differential equation. y(x) = En=o Cn (x + 1)" b) Find the smallest interval of convergence of a power series solution that is guaranteed by Theorem 6.2.1- Existence of Power Series Solution.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the differential equatione
(x² – 2x + 1)y" + xy' – y = 0
a) Show xo = -1 is an ordinary point of the differential equation.
y(x) = En=0 Cn (x + 1)"
b) Find the smallest interval of convergence of a power series solution
that is guaranteed by Theorem 6.2.1- Existence of Power Series Solution.
Transcribed Image Text:Consider the differential equatione (x² – 2x + 1)y" + xy' – y = 0 a) Show xo = -1 is an ordinary point of the differential equation. y(x) = En=0 Cn (x + 1)" b) Find the smallest interval of convergence of a power series solution that is guaranteed by Theorem 6.2.1- Existence of Power Series Solution.
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