Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Consider the differential equation

(x2−1)y′′+[1−(a+b)]xy′+aby=0, (11.7.9)

where a and b are constants.

O Show that the coefficients in a series solution to
Equation (11.7.9) centered at x = 0 must satisfy
the recurrence relation
(п — а)(п — b)
ал+2
-аn, п 3D 0, 1, ,
(n + 2)(n + 1)
and determine two linearly independent series
solutions.
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Transcribed Image Text:O Show that the coefficients in a series solution to Equation (11.7.9) centered at x = 0 must satisfy the recurrence relation (п — а)(п — b) ал+2 -аn, п 3D 0, 1, , (n + 2)(n + 1) and determine two linearly independent series solutions.
Expert Solution
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Step 1

Given, the differential equation

Calculus homework question answer, step 1, image 1

We have to calculate the recurrence relation and tow LI solutions of the differential equation.

Step 2

 Let the power series solution is

Calculus homework question answer, step 2, image 1

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