Find the temperature u(x, t) for the boundary-value problem dx² = ди at' 0 < x < L, t> 0 u(0, t) = 0, u(L, t) = 0, t > 0 u(x, 0) = f(x), 0 < x < L when L = 1 and f(x) = 100 sin(67x). [Hint: Look closely at Un = X(x)T(t) = A„e-k(n²77²/L³)t sin(17x) u(x, t) = and u(x, 0) = f(x) = A sin(N7T x).]
Find the temperature u(x, t) for the boundary-value problem dx² = ди at' 0 < x < L, t> 0 u(0, t) = 0, u(L, t) = 0, t > 0 u(x, 0) = f(x), 0 < x < L when L = 1 and f(x) = 100 sin(67x). [Hint: Look closely at Un = X(x)T(t) = A„e-k(n²77²/L³)t sin(17x) u(x, t) = and u(x, 0) = f(x) = A sin(N7T x).]
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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![Find the temperature u(x, t) for the boundary-value problem
a²u du
dx²
at
=
u(x, t) =
0 < x < L, t> 0
u(0, t) = 0, u(L, t) = 0, t > 0
u(x, 0) = f(x), 0 < x < L
when L = 1 and f(x) = 100 sin(67x). [Hint: Look closely at un= X(X)T(t) = A„e-k(n²π²/L²)t sin(n)
(nt x)
in(n7x).]
and u₁(x, 0) = f(x) = An sin t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c47eb58-11c8-4f3d-a446-35857f47e26f%2F4e380e13-f21c-40ac-bf11-a3059350f1c0%2F2e859fe_processed.png&w=3840&q=75)
Transcribed Image Text:Find the temperature u(x, t) for the boundary-value problem
a²u du
dx²
at
=
u(x, t) =
0 < x < L, t> 0
u(0, t) = 0, u(L, t) = 0, t > 0
u(x, 0) = f(x), 0 < x < L
when L = 1 and f(x) = 100 sin(67x). [Hint: Look closely at un= X(X)T(t) = A„e-k(n²π²/L²)t sin(n)
(nt x)
in(n7x).]
and u₁(x, 0) = f(x) = An sin t
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