2. Consider the heat equation du k- for 0 < x < L, and t > 0 with the boundary conditions u(0, t) = 0 and u(L, t) = 0, for t> 0. Solve for the following initial value conditions: a) f(x) = 4 sin (9ra L 1 b) f(x) = x € (0, L/2] x € (L/2, L)
2. Consider the heat equation du k- for 0 < x < L, and t > 0 with the boundary conditions u(0, t) = 0 and u(L, t) = 0, for t> 0. Solve for the following initial value conditions: a) f(x) = 4 sin (9ra L 1 b) f(x) = x € (0, L/2] x € (L/2, L)
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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![2. Consider the heat equation
ди
k-
for 0 < x < L, and t > 0
with the boundary conditions
u(0, t) = 0 and u(L, t) = 0, for t > 0.
Solve for the following initial value conditions:
a) f(x) = 4 sin (
1
b) f(x) =
x € (0, L/2]
x € (L/2, L)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6987145b-ac10-4a4b-9c55-4f1cc0c953d9%2Fcdbc6fee-8512-477c-a604-508039714386%2Fci98wcr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the heat equation
ди
k-
for 0 < x < L, and t > 0
with the boundary conditions
u(0, t) = 0 and u(L, t) = 0, for t > 0.
Solve for the following initial value conditions:
a) f(x) = 4 sin (
1
b) f(x) =
x € (0, L/2]
x € (L/2, L)
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