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Find two power series solutions of the given differential equation about the ordinary point x = 0. y" + 8xy' + 8y = 0 Oy₁ = 1 + 4x²8x4 + 32 6 Oy₁ = 1 - 4x² + 8x4 - 3²2x6- . Oy₁ = 1 - 4x² + 8x4 - 320x6. Oy₁ = 1 - 4x² - 8x4 - 32x6 -... 32 Oy₁ = 14x²8x² -33x6- 8 and y₂ = x-x³₁ and y₂ = x + and y₂ = x - and y₂ = x + W co w 8 +³ 8,3 w 00 W 00 8 + + + 64 5 15 64 -x² + 15 64,5 15 + -x + 15 64 5 512 and Y₂ = x-x³+₁ 8.3 64 15 5127 +... 105 sta 512 Ex² + ... 105 5127 +... 105 105 512 7 105 +.... +

Find two power series solutions of the given differential equation about the ordinary point x = 0. y" + 8xy' + 8y = 0 Oy₁ = 1 + 4x²8x4 + 32 6 Oy₁ = 1 - 4x² + 8x4 - 3²2x6- . Oy₁ = 1 - 4x² + 8x4 - 320x6. Oy₁ = 1 - 4x² - 8x4 - 32x6 -... 32 Oy₁ = 14x²8x² -33x6- 8 and y₂ = x-x³₁ and y₂ = x + and y₂ = x - and y₂ = x + W co w 8 +³ 8,3 w 00 W 00 8 + + + 64 5 15 64 -x² + 15 64,5 15 + -x + 15 64 5 512 and Y₂ = x-x³+₁ 8.3 64 15 5127 +... 105 sta 512 Ex² + ... 105 5127 +... 105 105 512 7 105 +.... +

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" + 8xy' + 8y = 0 4 6 Oy₁ = 1 + 4x² − 8x² + 32 xº + 3 Oy₁ = 1 - 4x² + 8x4. -322x6 - -X+... and Y₂ = x - Oy₁ = 1 - 4x² + 8x4 - 32x6 + Oy₁ = 1 - 4x² - 8x4 - 32 6 3 Oy₁ = 1 - 4x² - 8x² - 32²x6 - .... and y₂ = x + 8 ∞0 m and y₂ = x - +³+ 3 8 I'm and y₂ = x - x 8.3 3 + I'm ∞o I'm + 64 5 15 + 64 15 8.3 and y₂ = x + x² + -X + 64.5 15 64 5 15 x5 + 64. 5 15 512 105 512 105 ²x² + 512 105 +... 512 7 <+² 105 512 105 x² + ... +... +
Transcribed Image Text:Find two power series solutions of the given differential equation about the ordinary point x = 0. y" + 8xy' + 8y = 0 4 6 Oy₁ = 1 + 4x² − 8x² + 32 xº + 3 Oy₁ = 1 - 4x² + 8x4. -322x6 - -X+... and Y₂ = x - Oy₁ = 1 - 4x² + 8x4 - 32x6 + Oy₁ = 1 - 4x² - 8x4 - 32 6 3 Oy₁ = 1 - 4x² - 8x² - 32²x6 - .... and y₂ = x + 8 ∞0 m and y₂ = x - +³+ 3 8 I'm and y₂ = x - x 8.3 3 + I'm ∞o I'm + 64 5 15 + 64 15 8.3 and y₂ = x + x² + -X + 64.5 15 64 5 15 x5 + 64. 5 15 512 105 512 105 ²x² + 512 105 +... 512 7 <+² 105 512 105 x² + ... +... +
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