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Consider the following boundary-value problem: ²u²u + Ər² Əy² u(0, y) = 0 and u(1, y) = 0, y> 0, u(x,y) → 0, as y → +∞ u(x,0) = 1 00 • (1) (2) (3) (L)

Consider the following boundary-value problem: ²u²u + Ər² Əy² u(0, y) = 0 and u(1, y) = 0, y> 0, u(x,y) → 0, as y → +∞ u(x,0) = 1 00 • (1) (2) (3) (L)

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 * Consider the following boundary-value problem : au u 0, 0 < x < 1, y > 0 (1) Əx² u(0, y) = 0 and u(1, y) = 0, y > 0, (2) (L) u(x, y) → 0, as y → +0 (3) u(x, 0) = 1 0 < x < 1 (4) (1) By using the method of separation of variables, the family of solutions un(x, y) for equations (1), (2) and (3) is a. Un(x, y) = Bne-n*y sin(nax) b. иn (т, у) — Влe" -nay cos(nT2) %3D c. Un(x, y) = Bne¯naz cos(nTy) d. None of the above +o0 (2) Let u(x, y = Um(x, y) be a solution of (L). By using the initial condition (4), we obtain that a. B2n+1 = 0 and B2n b. B2n = 0 and B2n+1 4 %3D (2n+1)7° 8 с. Вл %3D (2n + 1)²7' d. None of the above
Transcribed Image Text:Problem 2 * Consider the following boundary-value problem : au u 0, 0 < x < 1, y > 0 (1) Əx² u(0, y) = 0 and u(1, y) = 0, y > 0, (2) (L) u(x, y) → 0, as y → +0 (3) u(x, 0) = 1 0 < x < 1 (4) (1) By using the method of separation of variables, the family of solutions un(x, y) for equations (1), (2) and (3) is a. Un(x, y) = Bne-n*y sin(nax) b. иn (т, у) — Влe" -nay cos(nT2) %3D c. Un(x, y) = Bne¯naz cos(nTy) d. None of the above +o0 (2) Let u(x, y = Um(x, y) be a solution of (L). By using the initial condition (4), we obtain that a. B2n+1 = 0 and B2n b. B2n = 0 and B2n+1 4 %3D (2n+1)7° 8 с. Вл %3D (2n + 1)²7' d. None of the above
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