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Find two power series solutions of the given differential equation about the ordinary point x = 0. y" 5xy' + y = 0 + x² + 11x4 + 77x6 2 24 240 Oy₁ = 1 + ₁ = 1 - 2 1=1-2/2² - Oy₂ = 1 + Oy₁ = 1- x ² + 3x8 8 3x4 8 11x4 24 3x4 8 19x12 80 19x6 80 + 77x5 240 19x6 80 + 1 +... and y₂ = x + x³ +. and and and and Y₂ = x + - Y₂= = x + Y₂ Y₂ 2x³ 3 = x + 4x5 5 2x5 7x⁹ 15 3 = x + x³ + + + 7x5 15 + + 7x5 15 + + 52x7 105 + 4x13 15 4x7 15 + 4x7 15 4x 52x7 5 105 + + +

Find two power series solutions of the given differential equation about the ordinary point x = 0. y" 5xy' + y = 0 + x² + 11x4 + 77x6 2 24 240 Oy₁ = 1 + ₁ = 1 - 2 1=1-2/2² - Oy₂ = 1 + Oy₁ = 1- x ² + 3x8 8 3x4 8 11x4 24 3x4 8 19x12 80 19x6 80 + 77x5 240 19x6 80 + 1 +... and y₂ = x + x³ +. and and and and Y₂ = x + - Y₂= = x + Y₂ Y₂ 2x³ 3 = x + 4x5 5 2x5 7x⁹ 15 3 = x + x³ + + + 7x5 15 + + 7x5 15 + + 52x7 105 + 4x13 15 4x7 15 + 4x7 15 4x 52x7 5 105 + + +

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" 5xy' + y = 0 + x² + 11x4 + 77x6 2 24 240 Oy₁ = 1 + ₁ = 1 - 2 1=1-2/2² - Oy₂ = 1 + Oy₁ = 1- x ² + 3x8 8 3x4 8 11x4 24 3x4 8 19x12 80 19x6 80 + 77x5 240 19x6 80 + 1 +... and y₂ = x + x³ +. and and and and Y₂ = x + - Y₂= = x + Y₂ Y₂ 2x³ 3 = x + 4x5 5 2x5 7x⁹ 15 3 = x + x³ + + + 7x5 15 + + 7x5 15 + + 52x7 105 + 4x13 15 4x7 15 + 4x7 15 4x 52x7 5 105 + + +
Transcribed Image Text:Find two power series solutions of the given differential equation about the ordinary point x = 0. y" 5xy' + y = 0 + x² + 11x4 + 77x6 2 24 240 Oy₁ = 1 + ₁ = 1 - 2 1=1-2/2² - Oy₂ = 1 + Oy₁ = 1- x ² + 3x8 8 3x4 8 11x4 24 3x4 8 19x12 80 19x6 80 + 77x5 240 19x6 80 + 1 +... and y₂ = x + x³ +. and and and and Y₂ = x + - Y₂= = x + Y₂ Y₂ 2x³ 3 = x + 4x5 5 2x5 7x⁹ 15 3 = x + x³ + + + 7x5 15 + + 7x5 15 + + 52x7 105 + 4x13 15 4x7 15 + 4x7 15 4x 52x7 5 105 + + +
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