Verify that the formulas for the Bessel functions

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Problem 14E Chapter 4.8

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 14E

PROBLEM 14E

Verify that the formulas for the Bessel functions J1/2(t),Y1/2(t) do indeed solve equation (16).

Step-by-Step Solution:

Solution

Step 1 of 5</p>

In this problem we have to verify that the formulas for the bessel functions solve the given equation.

Step 2 of 5</p>

Verifying the first formula

Neglecting constant we can consider the formula as  

Differentiating with respect to t, we get

,

Bessel equation of order

Step 3 of 5</p>

Substituting the formula in the equation we get

Thus  is the solution.

Step 4 of 5

Chapter 4.8, Problem 14E is Solved
Step 5 of 5

Textbook: Fundamentals of Differential Equations
Edition: 8th
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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