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Chapter 6: Q13RP (page 276)

In Problems 9-14 use an appropriate infinite series method about X = 0to find two solutions of the given differential equation.

Short Answer

Expert verified

Therefore the solution is

Step by step solution

01

Given Information

The given value is

02

Use Differentiate

Differentiating (*). we ge

03

Substitute the equation

Replacing the (1) and equation (2) in the initial differential equation, we get.

For the first summation, we let K = n -1. For the second summation, we let K = n Hence

04

Identity property

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Most popular questions from this chapter

In Problems 23 and 24 use the procedure in Example 8 to find two power series solutions of the given differential equation about the ordinary point

x=0y''+(sinx)y=0

In Problems, 3–6 find two power series solutions of the given differential equation about the ordinary point x 5 0. Compare the series solutions with the solutions of the differential equations obtained using the method of Section 4.3. Try to explain any differences between the two forms of the solutions.

Bessel’s Equation

In Problems 1-6 use (1) to find the general solution of the given differential equation on (0,∞).

4x2y+4xy'+(4x2-25)y=0

In Problems 15–24, x = 0is a regular singular point of the givendifferential equation. Show that the indicial roots of the singularity do not differ by an integer. Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on 0,∞.2xy"-y'+2y=0

In Problems, 7-18 find two power series solutions of the given differential equation about the ordinary point (x2-1)y''+xy'-y=0
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