The differential equation y'' - 2xy' + 2y = 0 is known as Hermites equation of order

Question:

The differential equation

y'' - 2xy' + 2αy = 0

is known as Hermite’s equation of order α after the French mathematician Charles Hermite (1822-1901). Show that the general solution of the equation is y(x) = c₀y₁(x), + c₁y₂(x), where

24a(a - 2)... (a - 2k + 2) 2k y(x) = 1 + (-1)* (2k)! k=1 2 (a-1)(a-3).. .(a- 2k+ 1) 2k+1 y2(x) = x + E(-1)* (2k + 1)! k=1

are power series solutions centered at the ordinary point 0.

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A First Course in Differential Equations with Modeling Applications

ISBN: 978-1111827052

10th edition

Authors: Dennis G. Zill

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Question Posted: Oct 29, 2020 08:53 AM

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The differential equation y'' - 2xy' + 2y = 0 is known as Hermites equation of order

Question:

24a(a - 2)... (a - 2k + 2) 2k y(x) = 1 + (-1)* (2k)! k=1 2 (a-1)(a-3).. .(a- 2k+ 1) 2k+1 y2(x) = x + E(-1)* (2k + 1)! k=1

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A First Course in Differential Equations with Modeling Applications

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