A3 Find a series expansion, up to x6, for the general solution of Hermite's equation: y" - xy' + sy = 0. Write the expansions for the specific solutions y₁, y2, satisfying y₁ (0) = 1, y₁ (0) = 0 and y2 (0) = 0, ; 3₂(0) = 1. Use the recurrence relation to show that the series for either y₁ or for y2 truncates to a polynomial if s is a positive integer. Write down the explicit forms of the expansions for y₁ and y2 for each of the cases s 3 and s = 4.
A3 Find a series expansion, up to x6, for the general solution of Hermite's equation: y" - xy' + sy = 0. Write the expansions for the specific solutions y₁, y2, satisfying y₁ (0) = 1, y₁ (0) = 0 and y2 (0) = 0, ; 3₂(0) = 1. Use the recurrence relation to show that the series for either y₁ or for y2 truncates to a polynomial if s is a positive integer. Write down the explicit forms of the expansions for y₁ and y2 for each of the cases s 3 and s = 4.
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:A3 Find a series expansion, up to x6, for the general solution of Hermite's equation:
y" - xy' + sy = 0.
Write the expansions for the specific solutions y₁, y2, satisfying
y₁ (0) = 1, y₁ (0) = 0 and y2 (0) = 0, ; 3₂(0) = 1.
Use the recurrence relation to show that the series for either y₁ or for y2 truncates
to a polynomial if s is a positive integer.
Write down the explicit forms of the expansions for y₁ and y2 for each of the cases
s 3 and s = 4.
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