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Л(г) %3 52 Tn+ 1)!n!2?n 2n (-1)"r2n J1 (1) n=0

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Differential equations problem.

The Bessel equation of order one is given by:

x^2y'' +xy' +(x^2 -1)y =0

A. Show that x=0 is a regular single point

B. Show that one solution for x>0 is

(see attached solution)

The function J₁ is known as the Bessel function of the first kind of order one.

C. Show that the series for J₁(x) converges for all x.

Л(г) %3
52 Tn+ 1)!n!2?n
2n
(-1)"r2n
J1 (1)
n=0

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