A- Use the separated solutions to solve the Laplace equation. in the region 00 given the boundary conditions (a) u=0 on x = 0 and x 1 (y 0) (b) i - 0 as y→ (c) u = sin (Tx) on y = 0 (0

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Author:Erwin Kreyszig
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Use both the d'Alembert solution and the separation of variables method and show that
A- Use the separated solutions to solve the Laplace equation.
in the region 0 Ex1, y>0given the boundary
conditions
(a) u=0 on x 0 and x 1 (y> 0)
(b) i →0 as y
(c) u = sin (Tx) on y 0
(0x成 1)
(0 <x系 1)
(Note: the identity sin e= (sin 50- 5 sin 30+
10 sin 6).)
B-Solve the wave equation
du 1du
dx ar
subject to the initial conditions
(a) utx, 0) = sinx (all x)
些(x,0) = 0
(b)
(all x)
they both give the same result.
Transcribed Image Text:Use both the d'Alembert solution and the separation of variables method and show that A- Use the separated solutions to solve the Laplace equation. in the region 0 Ex1, y>0given the boundary conditions (a) u=0 on x 0 and x 1 (y> 0) (b) i →0 as y (c) u = sin (Tx) on y 0 (0x成 1) (0 <x系 1) (Note: the identity sin e= (sin 50- 5 sin 30+ 10 sin 6).) B-Solve the wave equation du 1du dx ar subject to the initial conditions (a) utx, 0) = sinx (all x) 些(x,0) = 0 (b) (all x) they both give the same result.
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