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
are power series solutions centered at the ordinary point 0.
Transcribed Image Text:
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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Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1111827052
10th edition
Authors: Dennis G. Zill
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