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Solved: It can be shown that J0 has infinitely many zeros for x > 0. In particular, the

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

Solution for problem 14 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 14

It can be shown that J0 has infinitely many zeros for x > 0. In particular, the first threezeros are approximately 2.405, 5.520, and 8.653 (see Figure 5.7.1). Let j, j = 1, 2, 3, ... ,denote the zeros of J0; it follows thatJ0(jx) =1, x = 0,0, x = 1.Verify that y = J0(jx) satisfies the differential equationy +1xy + 2j y = 0, x > 0.Hence show that 10xJ0(ix)J0(jx) dx = 0 if i = j.This important property of J0(ix), which is known as the orthogonality property, is usefulin solving boundary value problems.Hint: Write the differential equation for J0(ix). Multiply it by xJ0(jx) and subtract itfrom xJ0(ix) times the differential equation for J0(jx). Then integrate from 0 to 1.

Step-by-Step Solution:
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Chapter 5.7, Problem 14 is Solved
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Textbook: Elementary Differential Equations
Edition: 10
Author: William E. Boyce, Richard C. DiPrima
ISBN: 9780470458327

The answer to “It can be shown that J0 has infinitely many zeros for x > 0. In particular, the first threezeros are approximately 2.405, 5.520, and 8.653 (see Figure 5.7.1). Let j, j = 1, 2, 3, ... ,denote the zeros of J0; it follows thatJ0(jx) =1, x = 0,0, x = 1.Verify that y = J0(jx) satisfies the differential equationy +1xy + 2j y = 0, x > 0.Hence show that 10xJ0(ix)J0(jx) dx = 0 if i = j.This important property of J0(ix), which is known as the orthogonality property, is usefulin solving boundary value problems.Hint: Write the differential equation for J0(ix). Multiply it by xJ0(jx) and subtract itfrom xJ0(ix) times the differential equation for J0(jx). Then integrate from 0 to 1.” is broken down into a number of easy to follow steps, and 121 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 61 chapters, and 1655 solutions. This textbook survival guide was created for the textbook: Elementary Differential Equations, edition: 10. Since the solution to 14 from 5.7 chapter was answered, more than 205 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 14 from chapter: 5.7 was answered by , our top Math solution expert on 03/13/18, 08:19PM. Elementary Differential Equations was written by and is associated to the ISBN: 9780470458327.

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