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Find a second solution of Bessels equation of order one by computing the cn(r2) and aof

Elementary Differential Equations | 10th Edition | ISBN: 9780470458327 | Authors: William E. Boyce, Richard C. DiPrima ISBN: 9780470458327 393

Solution for problem 11 Chapter 5.7

Elementary Differential Equations | 10th Edition

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Elementary Differential Equations | 10th Edition | ISBN: 9780470458327 | Authors: William E. Boyce, Richard C. DiPrima

Elementary Differential Equations | 10th Edition

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Problem 11

Find a second solution of Bessels equation of order one by computing the cn(r2) and aof Eq. (24) of Section 5.6 according to the formulas (19) and (20) of that section. Someguidelines along the way of this calculation are the following. First, use Eq. (24) of thissection to show that a1(1) and a1(1) are 0. Then show that c1(1) = 0 and, from therecurrence relation, that cn(1) = 0 for n = 3, 5, .... Finally, use Eq. (25) to show thata2(r) = a0(r + 1)(r + 3), a4(r) = a0(r + 1)(r + 3)(r + 3)(r + 5)and thata2m(r) = (1)ma0(r + 1)(r + 2m 1)(r + 3)(r + 2m + 1), m 3.Then show thatc2m(1) = (1)m+1(Hm + Hm1)/22mm!(m 1)!, m 1.

Step-by-Step Solution:
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L14 - 10 NOTE: x y = e (a,e ) 2 ex. Find g (x)f i g(x)= ex +2 e + xe + x . 2 e Now You Try It (NYTI): Find...

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Chapter 5.7, Problem 11 is Solved
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Textbook: Elementary Differential Equations
Edition: 10
Author: William E. Boyce, Richard C. DiPrima
ISBN: 9780470458327

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Find a second solution of Bessels equation of order one by computing the cn(r2) and aof

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