Find two power series solutions of the given differential equation about the ordinary point x = 0. (x² + 1)y" - 6y=0 Oy₁ = 1 + 3x² + x² − ³x6 + 1,6 Oy₁ = 1 + 3x² + 5x4 + 7x5 + Oy₁ = 1 + 3x² + x² + and y₂ = x + x³ ... and y₂ = x + 2x³ + 3x5 + 4x² + and y₂ = x - x³ 8 Oy₁ = 1 + x² + x²-16x Oy₁ = 1-3x² + 5x4 − 7x6 6 ... and y₂ = x + x+² and y₂ = x - 2x³ + 3x5 - 4x² + ...
Find two power series solutions of the given differential equation about the ordinary point x = 0. (x² + 1)y" - 6y=0 Oy₁ = 1 + 3x² + x² − ³x6 + 1,6 Oy₁ = 1 + 3x² + 5x4 + 7x5 + Oy₁ = 1 + 3x² + x² + and y₂ = x + x³ ... and y₂ = x + 2x³ + 3x5 + 4x² + and y₂ = x - x³ 8 Oy₁ = 1 + x² + x²-16x Oy₁ = 1-3x² + 5x4 − 7x6 6 ... and y₂ = x + x+² and y₂ = x - 2x³ + 3x5 - 4x² + ...
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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Transcribed Image Text:Find two power series solutions of the given differential equation about the ordinary point x = 0.
(x2+1)y" 6y = 0
Oy₁ = 1 + 3x² + x²-to
1,6
Oy₁ = 1 + 3x² + 5x4 + 7x6 +
Oy₁ = 1 + 3x² + x4 +
+6
5
+
+
and y₂ = x + x³
and Y2 = x + 2x³ + 3x5 + 4x7.
and y₂ = x - x³
34
₁=1+²+x+6+ ... and y₂ = x+3x²
Oy₁ = 1 - 3x² + 5x4 – 7x6 +
and y₂ = x - 2x³ + 3x5 - 4x² + .
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