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(a) Let 0 << X. Find a Fourier cosine series for S(x - ), where 8(x) is the Dirac delta function, valid for 0 < x < X. (b) Now solve the boundary value problem: A"(y) — X²A(y) = S(y - E), 0<

(a) Let 0 << X. Find a Fourier cosine series for S(x - ), where 8(x) is the Dirac delta function, valid for 0 < x < X. (b) Now solve the boundary value problem: A"(y) — X²A(y) = S(y - E), 0<

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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(a) Let 0 << X. Find a Fourier cosine series for 8(x-), where 8(x) is the Dirac delta function, valid for 0 < x < X. (b) Now solve the boundary value problem: A" (y) — X²A(y) = 8(y-E), 0<<Y,) A'(0) = A'(Y) = 0, 0<$<x;} where is a constant parameter and denotes differentiation with respect to y. Simplify your answer as far as possible.
Transcribed Image Text:(a) Let 0 << X. Find a Fourier cosine series for 8(x-), where 8(x) is the Dirac delta function, valid for 0 < x < X. (b) Now solve the boundary value problem: A" (y) — X²A(y) = 8(y-E), 0<<Y,) A'(0) = A'(Y) = 0, 0<$<x;} where is a constant parameter and denotes differentiation with respect to y. Simplify your answer as far as possible.
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