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(x² + 2)y" + 3xy' - y = 0 23-7 a. y = a₁ [1 + 4.4! 8-6! 23-7 b. y = α₁ [x+ ²x³. + ·x7 8-6! 23-7 c. y = ao x + x² + ·x² 4 8-6! 23-7 d. y = a₁ [1 + ¹x². ao + ·x6. 8-6! I ENEMINE 7 7 7 +1 x5 +5 ·x4 + 1 ao + 2-5! 14 2-5! •·] + α₁ [x = ² x ³. ·]· | + ao [1 − ²x² +3 | + α₁ [1 - ² x ..] + α₁₂ [x = ²/² x ² 14 x² + 2-5! 14 - + 2-5! -x4 -x4 x5 - 34-14 4-7! 34-14 4-7! 34-14 4-7! 34-14 4-7! x7 x6 +6 "x7 —* -⠀ -⠀

(x² + 2)y" + 3xy' - y = 0 23-7 a. y = a₁ [1 + 4.4! 8-6! 23-7 b. y = α₁ [x+ ²x³. + ·x7 8-6! 23-7 c. y = ao x + x² + ·x² 4 8-6! 23-7 d. y = a₁ [1 + ¹x². ao + ·x6. 8-6! I ENEMINE 7 7 7 +1 x5 +5 ·x4 + 1 ao + 2-5! 14 2-5! •·] + α₁ [x = ² x ³. ·]· | + ao [1 − ²x² +3 | + α₁ [1 - ² x ..] + α₁₂ [x = ²/² x ² 14 x² + 2-5! 14 - + 2-5! -x4 -x4 x5 - 34-14 4-7! 34-14 4-7! 34-14 4-7! 34-14 4-7! x7 x6 +6 "x7 —* -⠀ -⠀

Advanced Engineering Mathematics
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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Power Series
Find the Power series solution for the given differential equations centered at 0
(x² + 2)y" + 3xy' − y = 0 7 y = a₁ [1 + ²/2 23-7 a. -x² + -x6 8-6! 4.4! 7 1.3 23-7 b. y = α₁ x + ¹²x³ x5 ·x³ + -x7 4 4.4! 8-6! 7 23-7 ·x² + -x7 4.4! 8-6! c. y = a₁ [√x + d. y = a₁ [1 2 7 23-7 :x² + x4 4.4! 8-6! + X -x6 ao 6 ·] + a₁ [x = ² x³ + + ao [1. 2 ·x² + 6 +91 a₁ [1 - ² x x² + ··]- ·•.]. 1 + a₁ ₁ [x − ² x ³ + ₁ - —. 14 2-5! 14 2-5! 14 2-5! 14 2-5! 34-14 4-7! 34-14 4-7! 34-14 4-7! 34-14 5 x7 4-7! -x5 4 x -x4 x" "x² +6 26 —.
Transcribed Image Text:(x² + 2)y" + 3xy' − y = 0 7 y = a₁ [1 + ²/2 23-7 a. -x² + -x6 8-6! 4.4! 7 1.3 23-7 b. y = α₁ x + ¹²x³ x5 ·x³ + -x7 4 4.4! 8-6! 7 23-7 ·x² + -x7 4.4! 8-6! c. y = a₁ [√x + d. y = a₁ [1 2 7 23-7 :x² + x4 4.4! 8-6! + X -x6 ao 6 ·] + a₁ [x = ² x³ + + ao [1. 2 ·x² + 6 +91 a₁ [1 - ² x x² + ··]- ·•.]. 1 + a₁ ₁ [x − ² x ³ + ₁ - —. 14 2-5! 14 2-5! 14 2-5! 14 2-5! 34-14 4-7! 34-14 4-7! 34-14 4-7! 34-14 5 x7 4-7! -x5 4 x -x4 x" "x² +6 26 —.
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