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Solutions, if they exist, of equations of the form a,n (x)y(n) (x) + an-1(x)y(n-1)(x) +.. + a1 (x)y'(x) + ao(x)y(x) = f(x) are completely described by n linearly independent func- tions.

Solutions, if they exist, of equations of the form a,n (x)y(n) (x) + an-1(x)y(n-1)(x) +.. + a1 (x)y'(x) + ao(x)y(x) = f(x) are completely described by n linearly independent func- tions.

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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I know this is false but I need to prove it using the EXISTENCE AND UNIQUENESS THEOREM! Please do not copy from Chegg... I know the answer I just don't know how to apply the E&U theorem to prove it.

Solutions, if they exist, of equations of the form an(x)y(m) (x) + an-1(x)y(n-1)(x)+ ... + a1 (x)y'(x) + ao(x)y(x) = f(x) are completely described by n linearly independent func- tions.
Transcribed Image Text:Solutions, if they exist, of equations of the form an(x)y(m) (x) + an-1(x)y(n-1)(x)+ ... + a1 (x)y'(x) + ao(x)y(x) = f(x) are completely described by n linearly independent func- tions.
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