[16] Consider U₂ = Uzz + Uz, 0 0, u(0, t) = 0, u(a, t) = 0, u(x,0) = f(x), t> 0, 0≤x≤a. (a) Find all product functions of the form T(t)X(z) satisfying the PDE and the bound- ary conditions. (b) Find the general solution formula for u(x, t), in the form of eigenfunction expansion.
[16] Consider U₂ = Uzz + Uz, 0 0, u(0, t) = 0, u(a, t) = 0, u(x,0) = f(x), t> 0, 0≤x≤a. (a) Find all product functions of the form T(t)X(z) satisfying the PDE and the bound- ary conditions. (b) Find the general solution formula for u(x, t), in the form of eigenfunction expansion.
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
#16
![[16] Consider
Ut = Uxx + Uxy
0<x<a,t> 0,
u(0, t) = 0, u(a, t) = 0,
u(x,0) = f(x),
t> 0,
0≤x≤a.
(a) Find all product functions of the form T(t)X(r) satisfying the PDE and the bound-
ary conditions.
(b) Find the general solution formula for u(x, t), in the form of eigenfunction expansion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68164dd-6bba-4aa5-92bc-4824a71db092%2Ff66973c4-5af7-44c4-afe9-33e8d074c3d7%2Fv4m31j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[16] Consider
Ut = Uxx + Uxy
0<x<a,t> 0,
u(0, t) = 0, u(a, t) = 0,
u(x,0) = f(x),
t> 0,
0≤x≤a.
(a) Find all product functions of the form T(t)X(r) satisfying the PDE and the bound-
ary conditions.
(b) Find the general solution formula for u(x, t), in the form of eigenfunction expansion.
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