0) = cos x, uz(x,0) = e²+1 Use the d'Alembert solution to solve 6 UT 5 UTM Pu 1 Pu -00 < x < o0, t>0, 9 Əz² 5UTM UTM UT u(x, 0) = cos² x, u(x,0) = e*+1. 6 UTM TM UTM ở UTM

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
< 3.
QUESTION 3
M UTM
a) Use the d'Alembert solution to solve
& UTM
UTM
6 UTM
Pu
5 UTM
5 UTM & UTM 6 UTM
-0 < x < ∞, t>0,
& UTM
%3D
9 Əx²
= cos² x, u(x,0) = e"+1.
5 UTM
b) Solve the following heat equation by using the method of separation of
variables
& UTM & UTM UTM
5 UTM &UTM 61
M
du
= 2
with boundary conditions
& UTM
UTM 5 UTM
0 <x < 3, t> 0,
UTM
8 UTM U
5 UTM
6 UTM
u(0, t) = 0, u(3, t) = 0, t>0,
UTM &UTM UTM
& UTM
& UTM
IM & UTM & UTM
0< x < 3.
I UTM
u(x, 0) = 2+ x,
5 UTM & UTM
5 UTM
UTM UTM
Transcribed Image Text:< 3. QUESTION 3 M UTM a) Use the d'Alembert solution to solve & UTM UTM 6 UTM Pu 5 UTM 5 UTM & UTM 6 UTM -0 < x < ∞, t>0, & UTM %3D 9 Əx² = cos² x, u(x,0) = e"+1. 5 UTM b) Solve the following heat equation by using the method of separation of variables & UTM & UTM UTM 5 UTM &UTM 61 M du = 2 with boundary conditions & UTM UTM 5 UTM 0 <x < 3, t> 0, UTM 8 UTM U 5 UTM 6 UTM u(0, t) = 0, u(3, t) = 0, t>0, UTM &UTM UTM & UTM & UTM IM & UTM & UTM 0< x < 3. I UTM u(x, 0) = 2+ x, 5 UTM & UTM 5 UTM UTM UTM
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