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 equation for x >0. xy' +(1-x)y'-y=0 The equation has a general solution in the form c₁y₁ (x) +C2y2 (x) where y₁ (x) is obtained from the root of the associated indicial equation with the largest real value. If the second solution has a term with y₁ (x), then count that term as only one term. 3₁ (x)=+... and y2 (x)=+...
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 equation for x >0. xy' +(1-x)y'-y=0 The equation has a general solution in the form c₁y₁ (x) +C2y2 (x) where y₁ (x) is obtained from the root of the associated indicial equation with the largest real value. If the second solution has a term with y₁ (x), then count that term as only one term. 3₁ (x)=+... and y2 (x)=+...
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 the first three nonzero terms, or as many as exist, in the series expansion about x=0 for a general solution to the given equation for x >0.
xy' +(1-x)y'-y=0
C
The equation has a general solution in the form C₁ y₁ (x)+c2Y2 (x) where y₁ (x) is obtained from the root of the associated indicial equation with the largest real value. If the second solution has a term with y₁ (x), then
count that term as only one term.
Y₁ (x) =+ and y2 (x)=+...
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