4. Find the general solution of wt Wra + sin(x +t) by using the coordinate method.
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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Question
I need help with number 4
![1. Use the coordinate method to solve 2u, – Uy + (x + 2y)u = 0 with u(x,0) = e-2"/5,
2. Show that the steady state of the diffusion equation
Uz = Kugr, 0 <x < L, t> 0,
Uz (0, t) = uz(L, t) = 0,
u(x, 0) = $(x)
%3D
is given by
u,(2) =
1
$(x)dx.
3. Classify equation ugz +Uzt – 20ut = 0, and solve the equation with initial conditions:
u(x,0) = 6(x) and u;(x,0) = (x).
4. Find the general solution of wt = Wra + sin(x +t) by using the coordinate method.
5. Let L>1/2. Consider the diffusion equation
Uų = Kura, -L <x < L, t >0,
u(-L, t) — и(L, t) %3D0,
u(x,0)
4
%3D
By using the maximum principle to show
1
(a) Ju(x, t)| <
for -L <x <Land t 2 0;
12
(b) u(-x, t) =-u(x, t) for -L <a<L and t > 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe81da00a-4cea-4000-a024-f288b328857b%2F55c5196a-fd8e-4652-b787-12e2154d13e7%2Fggdaz1_processed.png&w=3840&q=75)
Transcribed Image Text:1. Use the coordinate method to solve 2u, – Uy + (x + 2y)u = 0 with u(x,0) = e-2"/5,
2. Show that the steady state of the diffusion equation
Uz = Kugr, 0 <x < L, t> 0,
Uz (0, t) = uz(L, t) = 0,
u(x, 0) = $(x)
%3D
is given by
u,(2) =
1
$(x)dx.
3. Classify equation ugz +Uzt – 20ut = 0, and solve the equation with initial conditions:
u(x,0) = 6(x) and u;(x,0) = (x).
4. Find the general solution of wt = Wra + sin(x +t) by using the coordinate method.
5. Let L>1/2. Consider the diffusion equation
Uų = Kura, -L <x < L, t >0,
u(-L, t) — и(L, t) %3D0,
u(x,0)
4
%3D
By using the maximum principle to show
1
(a) Ju(x, t)| <
for -L <x <Land t 2 0;
12
(b) u(-x, t) =-u(x, t) for -L <a<L and t > 0.
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