The indicial equation and recurrence relation for the differential equation x²y" + x[(2-b)+x]y- (b-yx)y 0 (11.5.37) are, respectively, (r + 1)(r – b) = 0, (r +n+ 1)(r + n - b)an = -[(r +n- 1) +y]an-1, n = 1, 2, 3, ..., in the usual notation, where b and y are constants. Determine the form of two linearly independent se- ries solutions to Equation (11.5.37) on (0, o0) in
The indicial equation and recurrence relation for the differential equation x²y" + x[(2-b)+x]y- (b-yx)y 0 (11.5.37) are, respectively, (r + 1)(r – b) = 0, (r +n+ 1)(r + n - b)an = -[(r +n- 1) +y]an-1, n = 1, 2, 3, ..., in the usual notation, where b and y are constants. Determine the form of two linearly independent se- ries solutions to Equation (11.5.37) on (0, o0) in
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q.b=−1.
![The indicial equation and recurrence relation for the
differential equation
x²y" + x[(2-b)+x]y- (b-yx)y 0 (11.5.37)
are, respectively,
(r + 1)(r – b) = 0,
(r +n+ 1)(r + n - b)an = -[(r +n- 1) +y]an-1,
n = 1, 2, 3, ...,
in the usual notation, where b and y are constants.
Determine the form of two linearly independent se-
ries solutions to Equation (11.5.37) on (0, o0) in](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51bb2c50-a6ab-4507-90b8-24cebd0a1383%2F81f4f76a-0464-48c6-b7a7-6046e51b7bd7%2F4cwq4x.jpeg&w=3840&q=75)
Transcribed Image Text:The indicial equation and recurrence relation for the
differential equation
x²y" + x[(2-b)+x]y- (b-yx)y 0 (11.5.37)
are, respectively,
(r + 1)(r – b) = 0,
(r +n+ 1)(r + n - b)an = -[(r +n- 1) +y]an-1,
n = 1, 2, 3, ...,
in the usual notation, where b and y are constants.
Determine the form of two linearly independent se-
ries solutions to Equation (11.5.37) on (0, o0) in
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