4. Consider the heat equation u k- ди for 0 < x < L, and t >0 with the boundary conditions du (0, t) = 0 and u(L,t) = 0, for t > 0. %3D Solve for the following initial value conditions: а) f(г) — х [1 0e (0, L/2] 2 1€ (L/2, L) b) f(x) =
4. Consider the heat equation u k- ди for 0 < x < L, and t >0 with the boundary conditions du (0, t) = 0 and u(L,t) = 0, for t > 0. %3D Solve for the following initial value conditions: а) f(г) — х [1 0e (0, L/2] 2 1€ (L/2, L) b) f(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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![4. Consider the heat equation
ди
k-
for 0 < x < L, and t > 0
with the boundary conditions
ди
(0, t) = 0 and u(L, t) = 0, for t> 0.
%3D
Solve for the following initial value conditions:
а) f(х) — х
S1 0€ (0, L/2]
1 (L/2, L)
b) f(x) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6987145b-ac10-4a4b-9c55-4f1cc0c953d9%2F5a3ff2a6-7026-4b21-a2e7-5a5ad69bb1ab%2Fy1mvdu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Consider the heat equation
ди
k-
for 0 < x < L, and t > 0
with the boundary conditions
ди
(0, t) = 0 and u(L, t) = 0, for t> 0.
%3D
Solve for the following initial value conditions:
а) f(х) — х
S1 0€ (0, L/2]
1 (L/2, L)
b) f(x) =
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