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Find the first three nonzero terms, or as many as exist, in the series expansion about x = 0 for a general solution to the given linear third-order equation for x > 0. 4x³y + 10x²y" +2(x+x²) y' + 2xy = 0

Find the first three nonzero terms, or as many as exist, in the series expansion about x = 0 for a general solution to the given linear third-order equation for x > 0. 4x³y + 10x²y" +2(x+x²) y' + 2xy = 0

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 the first three nonzero terms, or as many as exist, in the series expansion about x = 0 for a general solution to the given linear third-order equation for x > 0. 4x³y + 10x²y" + 2(x+x²)y' + 2xy =0 The general solution has the form y(x) = C₁V₁ (X) + C₂Y₂ (X) + C3Y3 (X). What are the first three terms for the series for the largest root of the indicial equation r₁?
Transcribed Image Text:Find the first three nonzero terms, or as many as exist, in the series expansion about x = 0 for a general solution to the given linear third-order equation for x > 0. 4x³y + 10x²y" + 2(x+x²)y' + 2xy =0 The general solution has the form y(x) = C₁V₁ (X) + C₂Y₂ (X) + C3Y3 (X). What are the first three terms for the series for the largest root of the indicial equation r₁?
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