3. Consider the heat equation ди k for 0 < x < L, and t > 0 with the boundary conditions ди (0, t) = 0 and ди (L,t) = 0, for t > 0. Solve for the following initial value conditions: a) f(x) = 2+ 3 cos (3T) L (1 0€ (0, L/2] b) f(x) = 1 (L/2, L)
3. Consider the heat equation ди k for 0 < x < L, and t > 0 with the boundary conditions ди (0, t) = 0 and ди (L,t) = 0, for t > 0. Solve for the following initial value conditions: a) f(x) = 2+ 3 cos (3T) L (1 0€ (0, L/2] b) f(x) = 1 (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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![3. Consider the heat equation
du
Pu
k
for 0 < x < L, and t > 0
with the boundary conditions
du
-(0, t) = 0 and
ди
(L,t) = 0, for t> 0.
Solve for the following initial value conditions:
a) f(x) = 2+ 3 cos
3TT)
L
(1
0€ (0, L/2]
b) f(x) =
2
1 (L/2, L)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6987145b-ac10-4a4b-9c55-4f1cc0c953d9%2Fc8964edc-7427-4f5a-980b-aae7615f434d%2Fd0ho53i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the heat equation
du
Pu
k
for 0 < x < L, and t > 0
with the boundary conditions
du
-(0, t) = 0 and
ди
(L,t) = 0, for t> 0.
Solve for the following initial value conditions:
a) f(x) = 2+ 3 cos
3TT)
L
(1
0€ (0, L/2]
b) f(x) =
2
1 (L/2, L)
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