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Find two power series solutions of the given differential equation about the ordinary point x = 0. y" + x²y' + xy = 0 Oy₁ = 1 Oy₁ = 1 Oy₁ = 1- Oy₁ = 1 - Oy₁ = 1 = 1 - 1 4 12 1 2 -x + + 2 5 672 1 4 -X + 8 5 1/2+³ +6 672 1+³+15 45 6 -X 8 14 8 and Y/₂ = x- and Y₂ = x and and Y₂ = x - Y/₂ = x - 1 3 3 1 10 1 + 1 3 -x+ + 5 1 15 + 1 5 and Y₂ = x-x² + 10 + 5 120 1 15 1 9 1 120 5 7 252 9

Find two power series solutions of the given differential equation about the ordinary point x = 0. y" + x²y' + xy = 0 Oy₁ = 1 Oy₁ = 1 Oy₁ = 1- Oy₁ = 1 - Oy₁ = 1 = 1 - 1 4 12 1 2 -x + + 2 5 672 1 4 -X + 8 5 1/2+³ +6 672 1+³+15 45 6 -X 8 14 8 and Y/₂ = x- and Y₂ = x and and Y₂ = x - Y/₂ = x - 1 3 3 1 10 1 + 1 3 -x+ + 5 1 15 + 1 5 and Y₂ = x-x² + 10 + 5 120 1 15 1 9 1 120 5 7 252 9

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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Find two power series solutions of the given differential equation about the ordinary point x = 0. y" + x²y' + xy = 0 Oy₁ = 1 Oy₁ = 1 Oy₁ = 1- Oy₁ = 1 - Oy₁ = 1 = 1 - 1 4 12 1 2 -x + 2 + 5 672 + 1 4 -X 8 1/2+³ 1+³+15 45 5 672 6 -X 14 8 8 +6 and Y₂ = x - and Y₂ = x - and Y₂ = X- and Y/₂ = x - 1 3 3 1 10 1 + 1 3 -x+ + 5 1 15 + 1 5 and Y₂ = x-x² + 10 + 5 120 1 15 1 9 1 120 5 7 252 9
Transcribed Image Text:Find two power series solutions of the given differential equation about the ordinary point x = 0. y" + x²y' + xy = 0 Oy₁ = 1 Oy₁ = 1 Oy₁ = 1- Oy₁ = 1 - Oy₁ = 1 = 1 - 1 4 12 1 2 -x + 2 + 5 672 + 1 4 -X 8 1/2+³ 1+³+15 45 5 672 6 -X 14 8 8 +6 and Y₂ = x - and Y₂ = x - and Y₂ = X- and Y/₂ = x - 1 3 3 1 10 1 + 1 3 -x+ + 5 1 15 + 1 5 and Y₂ = x-x² + 10 + 5 120 1 15 1 9 1 120 5 7 252 9
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