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2. Solve the wave equation c2 + dy? in two dimensional rectangular region 0 < x < L, 0 < y < H, subject to the initial conditions u(х, у, 0) — 0, ди (x, y,0) = f(x, y) and the following boundary conditions: a) u(0, y, t) = 0, u(L, y, t) 3 0, u(х, 0, 6) — 0, и(, Н, €) %3D 0 b) du ди u(0, y, t) = 0, u(L, y, t) = 0, (x,0, t) = 0, dy (a, H, t) = 0 dy

2. Solve the wave equation c2 + dy? in two dimensional rectangular region 0 < x < L, 0 < y < H, subject to the initial conditions u(х, у, 0) — 0, ди (x, y,0) = f(x, y) and the following boundary conditions: a) u(0, y, t) = 0, u(L, y, t) 3 0, u(х, 0, 6) — 0, и(, Н, €) %3D 0 b) du ди u(0, y, t) = 0, u(L, y, t) = 0, (x,0, t) = 0, dy (a, H, t) = 0 dy

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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2. Solve the wave equation c2 dy? in two dimensional rectangular region 0 < x < L, 0 < y < H, subject to the initial conditions du (x, y, 0) = f(x, y) u(х, у, 0) — 0, and the following boundary conditions: a) и(0, у, t) %3 0, u(L, y, t) 3 0, u(х, 0, 6) — 0, и(, H, €) %3D 0 b) du ди u(0, y, t) = 0, u(L, y, t) = 0, (x, 0, t) = 0, dy (a, H, t) = 0 dy
Transcribed Image Text:2. Solve the wave equation c2 dy? in two dimensional rectangular region 0 < x < L, 0 < y < H, subject to the initial conditions du (x, y, 0) = f(x, y) u(х, у, 0) — 0, and the following boundary conditions: a) и(0, у, t) %3 0, u(L, y, t) 3 0, u(х, 0, 6) — 0, и(, H, €) %3D 0 b) du ди u(0, y, t) = 0, u(L, y, t) = 0, (x, 0, t) = 0, dy (a, H, t) = 0 dy
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