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Problem 2. (6) Construct the Green's function for the modified Helmholtz equation: (² - 4²") y(x) = S(x) with finite asymptotic values. That is, find the function Gx(x) that is the solution of y"(x) - k₂²³ y(x) = S(x-x₁) with asseemning k³²>0. (b) Solve (d² - R²) X(X) = H(x+1) H(1-x) with lim Y(X) = 0.. shows ups in study of waver diffusion, etc. ·lim y(x) = 0₁. X-100

Problem 2. (6) Construct the Green's function for the modified Helmholtz equation: (² - 4²") y(x) = S(x) with finite asymptotic values. That is, find the function Gx(x) that is the solution of y"(x) - k₂²³ y(x) = S(x-x₁) with asseemning k³²>0. (b) Solve (d² - R²) X(X) = H(x+1) H(1-x) with lim Y(X) = 0.. shows ups in study of waver diffusion, etc. ·lim y(x) = 0₁. X-100

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 2 shows (0) Construct the Green's function for the modified Helmholtz equation: (d² - 4² ) y(x) = S(x) with finite asymptatic values. That is, find the function Ex(x) that is the solution of y"(x) - k² y(x) = S(x-x!) with lim y(x) = 0, asseinning R2² > 0. X→ ±00 (b) Solve (d² - R²³)×(x) = H(x+1) H(1-x) with lim Y(X) = 0. X(X) ups in study of waves, diffusion, etc.
Transcribed Image Text:Problem 2 shows (0) Construct the Green's function for the modified Helmholtz equation: (d² - 4² ) y(x) = S(x) with finite asymptatic values. That is, find the function Ex(x) that is the solution of y"(x) - k² y(x) = S(x-x!) with lim y(x) = 0, asseinning R2² > 0. X→ ±00 (b) Solve (d² - R²³)×(x) = H(x+1) H(1-x) with lim Y(X) = 0. X(X) ups in study of waves, diffusion, etc.
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