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Find a power series solution of the form y(x) = 0 Cnx" of the given differential equation. 700 n=0 x²y + y = 0 First compute y'(x) = 1 (Use cn for cn in your answer) Then x²y (x) + y = [*] x+ En=2 (Use c0 for co, c1 for c₁, cn for Cn and cnm1 for Cn-1 in your answer) Requiring that the terms of this series for x²y + y vanish gives Co = C₁ = Cn = xn-1 + Cn-1 for n ≥ 2 The series solution converges to the familiar function y = f(x) = xn

Find a power series solution of the form y(x) = 0 Cnx" of the given differential equation. 700 n=0 x²y + y = 0 First compute y'(x) = 1 (Use cn for cn in your answer) Then x²y (x) + y = [*] x+ En=2 (Use c0 for co, c1 for c₁, cn for Cn and cnm1 for Cn-1 in your answer) Requiring that the terms of this series for x²y + y vanish gives Co = C₁ = Cn = xn-1 + Cn-1 for n ≥ 2 The series solution converges to the familiar function y = f(x) = xn

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 solution of the form y(x) = 0 Cnx" of the given differential equation. n=0 x²y + y = 0 First compute y'(x) = 1 (Use cn for cn in your answer) Then x²y (x) + y = Co = C1 = Cn = xn-1 + ===x+ En=2 (Use c0 for co, c1 for c₁, cn for Cn and cnm1 for Cn-1 in your answer) Requiring that the terms of this series for x²y + y vanish gives 700 Cn-1 for n ≥ 2 The series solution converges to the familiar function y = f(x) = xn
Transcribed Image Text:Find a power series solution of the form y(x) = 0 Cnx" of the given differential equation. n=0 x²y + y = 0 First compute y'(x) = 1 (Use cn for cn in your answer) Then x²y (x) + y = Co = C1 = Cn = xn-1 + ===x+ En=2 (Use c0 for co, c1 for c₁, cn for Cn and cnm1 for Cn-1 in your answer) Requiring that the terms of this series for x²y + y vanish gives 700 Cn-1 for n ≥ 2 The series solution converges to the familiar function y = f(x) = xn
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