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, satisfyingy₁ (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 truncatesto a polynomial if s is a positive integer.Write down the explicit forms of the expansions for y₁ and y2 for each of the casess 3 and s = 4.

The objective of this question is to find a series expansion for the general solution of Hermite's…

Answered: A3 Find a series expansion, up to x6,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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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.
1

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