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Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equ (x + 8) y" +y = 0 y(X) = +.. (Type an expression in terms of a, and a, that includes all terms up to order 3.)

Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equ (x + 8) y" +y = 0 y(X) = +.. (Type an expression in terms of a, and a, that includes all terms up to order 3.)

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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**Problem Statement:** Find the first four nonzero terms in a power series expansion about \(x = 0\) for a general solution to the given differential equation. \[ \left( x^2 + 8 \right) y'' + y = 0 \] **Solution:** \(y(x) = \boxed{\phantom{a}} + \ldots\) (Type an expression in terms of \(a_0\) and \(a_1\) that includes all terms up to order 3.)
Transcribed Image Text:**Problem Statement:** Find the first four nonzero terms in a power series expansion about \(x = 0\) for a general solution to the given differential equation. \[ \left( x^2 + 8 \right) y'' + y = 0 \] **Solution:** \(y(x) = \boxed{\phantom{a}} + \ldots\) (Type an expression in terms of \(a_0\) and \(a_1\) that includes all terms up to order 3.)
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