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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40e9a683-3cab-42d7-bebb-56688785662a%2Fbc2a6c64-369b-4ace-89b8-85d89a27ca28%2Fj62fshl_processed.jpeg&w=3840&q=75)
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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