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Find a power series expansion about x = 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. ²z' + xz = 0 -z"

Find a power series expansion about x = 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. ²z' + xz = 0 -z"

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 a power series expansion about x = 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. -z" +x?z' + xz = 0 What is the power series solution to the differential equation? 2(-1)n (3-6.9...(3n)) (3n - 2)! E (- 1)r (1 •4 •7.-(3n – 2)) (3n + 2)! 3n + O A. Z(x) = ao 1+ +a, x+ Σ n=1 n=1 (1.4.7..(3n - 2)) 3n E (- 1)". (2•5.8..(3n - 1) E (- 1)"- 3n + 1 B. z(x) = ao 1+ + a, x+ X- (3n)! (3n + 1)! n=1 n=1 00 (3•6.9...(3n)) (1.4.7..(3n - 2)) 3n + 3n OC. z(x) = ao 1+ E +a, x+ E (3n - 2)! (3n + 2)! n=1 n=1 (2.5.8.(3n - 1)) 3n + 1 Σ (1.4.7...(3n - 2)) 3n D. z(x) = ao 1+ E + x+ (3n)! (3n + 1 + 1)! n=1 n=1
Transcribed Image Text:Find a power series expansion about x = 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. -z" +x?z' + xz = 0 What is the power series solution to the differential equation? 2(-1)n (3-6.9...(3n)) (3n - 2)! E (- 1)r (1 •4 •7.-(3n – 2)) (3n + 2)! 3n + O A. Z(x) = ao 1+ +a, x+ Σ n=1 n=1 (1.4.7..(3n - 2)) 3n E (- 1)". (2•5.8..(3n - 1) E (- 1)"- 3n + 1 B. z(x) = ao 1+ + a, x+ X- (3n)! (3n + 1)! n=1 n=1 00 (3•6.9...(3n)) (1.4.7..(3n - 2)) 3n + 3n OC. z(x) = ao 1+ E +a, x+ E (3n - 2)! (3n + 2)! n=1 n=1 (2.5.8.(3n - 1)) 3n + 1 Σ (1.4.7...(3n - 2)) 3n D. z(x) = ao 1+ E + x+ (3n)! (3n + 1 + 1)! n=1 n=1
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