Question 4 The equation y" – 2xy' + Ay = 0, 1 constant, is known as the Hermite differential equation, and it appears in many areas of mathematics and physics. (i) Find two linearly independent solutions of Hermite equation, (ii) Show that Hermite equation has a polynomial solution of degree n if 1 = 2n. This polynomial, when properly normalized, is known as Hermite polynomial Hn(x).
Question 4 The equation y" – 2xy' + Ay = 0, 1 constant, is known as the Hermite differential equation, and it appears in many areas of mathematics and physics. (i) Find two linearly independent solutions of Hermite equation, (ii) Show that Hermite equation has a polynomial solution of degree n if 1 = 2n. This polynomial, when properly normalized, is known as Hermite polynomial Hn(x).
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:Question 4
The equation y" – 2xy' + Ay = 0, 1 constant, is known as the
Hermite differential equation, and it appears in many
areas of mathematics and physics.
(i) Find two linearly independent solutions of Hermite
equation,
(ii) Show that Hermite equation has a polynomial solution
of degree n ifl= 2n. This polynomial, when properly
normalized, is known as Hermite polynomial Hn(x).
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