[13] Consider Ut - Uzz = 0, 0 0, u,(0, t) = 0, u(1, t) = 0, t> 0, u(x,0) = f(x), 0≤x≤ 1. (a) Find all product solutions u(x, t) = T(t)X(r) satisyfing the PDE and boundary conditions. (b) Find the general solution formula for u(x, t). (c) Solve the problem when f(x) = {1 0 ≤ x ≤ 1/2, 1/2 < x < 1.
[13] Consider Ut - Uzz = 0, 0 0, u,(0, t) = 0, u(1, t) = 0, t> 0, u(x,0) = f(x), 0≤x≤ 1. (a) Find all product solutions u(x, t) = T(t)X(r) satisyfing the PDE and boundary conditions. (b) Find the general solution formula for u(x, t). (c) Solve the problem when f(x) = {1 0 ≤ x ≤ 1/2, 1/2 < x < 1.
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
#13
Need A, B and C
![[13] Consider
Ut
Uzz = 0,
u(0, t) = 0, u(1, t) = 0,
u(x,0) = f(x),
0<x< 1,t> 0,
t> 0,
0≤x≤ 1.
=
T(t)X(x) satisyfing the PDE and boundary
(a) Find all product solutions u(x, t)
conditions.
(b) Find the general solution formula for u(x, t).
0 ≤ x ≤ 1/2,
(c) Solve the problem when f(x)= {
1/2 < x≤ 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68164dd-6bba-4aa5-92bc-4824a71db092%2Fb3dfe267-973c-4531-804e-4118c3f735ad%2Fkx1jt3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[13] Consider
Ut
Uzz = 0,
u(0, t) = 0, u(1, t) = 0,
u(x,0) = f(x),
0<x< 1,t> 0,
t> 0,
0≤x≤ 1.
=
T(t)X(x) satisyfing the PDE and boundary
(a) Find all product solutions u(x, t)
conditions.
(b) Find the general solution formula for u(x, t).
0 ≤ x ≤ 1/2,
(c) Solve the problem when f(x)= {
1/2 < x≤ 1.
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