Ju 2²u Consider the heat equation = Ət for a bar of length L=1, with non homogeneous boundary conditions: u(0,t) = 1 and u(1,t) = 3. The initial condition дх2 is u(x,0) = x. The problem is transformed into another one with homogeneous conditions, in terms of v=u-u, where u is the equilibrium solution of the u. Hence Əv 2²v and v(0,t) = 0 and v(1,t) = 0. Ət 2x² Hence, v(x,t) = Σ asin(n éx) e−(nä²t¸ Select the correct formula for an n=1 Select one: O a. 2 · 25 (2² (2x-1)sin(n πx) dx b.2f'( (-2x)sin(nπx) dx 25₁ (-x-1)sin(nπx) dx O O c. 2 O d. 2 f'x x sin(n πx) dx
Ju 2²u Consider the heat equation = Ət for a bar of length L=1, with non homogeneous boundary conditions: u(0,t) = 1 and u(1,t) = 3. The initial condition дх2 is u(x,0) = x. The problem is transformed into another one with homogeneous conditions, in terms of v=u-u, where u is the equilibrium solution of the u. Hence Əv 2²v and v(0,t) = 0 and v(1,t) = 0. Ət 2x² Hence, v(x,t) = Σ asin(n éx) e−(nä²t¸ Select the correct formula for an n=1 Select one: O a. 2 · 25 (2² (2x-1)sin(n πx) dx b.2f'( (-2x)sin(nπx) dx 25₁ (-x-1)sin(nπx) dx O O c. 2 O d. 2 f'x x sin(n πx) dx
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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course partial differential equations
![Consider the heat equation
ди 2²u
Ət
is u(x,0) = x.
for a bar of length L=1, with non homogeneous boundary conditions: u(0,t) = 1 and u(1,t) = 3. The initial condition
2x².
The problem is transformed into another one with homogeneous conditions, in terms of v=u-UE, where UE is the equilibrium solution of the u. Hence
Əv
2²v
= and v(0,t) = 0 and v(1,t) = 0.
Ət
2x²
Hence, v(x,t) = Ž asin(n éx) e ¯
2-(nπ)²t
. Select the correct formula for an
n=1
Select one:
O a. 2
3. 2 √ (2)
(2x-1)sin(nπx) dx
O b. 2
0.2 *(-2x)sin(n Tx) dx
0 c.2f" (-x-1)sin(nπx) dx
O
d.2 f'xs
x sin(nπx) dx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb26ce4d0-1614-425e-b603-50b6ac3f59a0%2F7e9fd03a-c17c-419f-8987-4f92d43e340e%2Fcv30xg_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the heat equation
ди 2²u
Ət
is u(x,0) = x.
for a bar of length L=1, with non homogeneous boundary conditions: u(0,t) = 1 and u(1,t) = 3. The initial condition
2x².
The problem is transformed into another one with homogeneous conditions, in terms of v=u-UE, where UE is the equilibrium solution of the u. Hence
Əv
2²v
= and v(0,t) = 0 and v(1,t) = 0.
Ət
2x²
Hence, v(x,t) = Ž asin(n éx) e ¯
2-(nπ)²t
. Select the correct formula for an
n=1
Select one:
O a. 2
3. 2 √ (2)
(2x-1)sin(nπx) dx
O b. 2
0.2 *(-2x)sin(n Tx) dx
0 c.2f" (-x-1)sin(nπx) dx
O
d.2 f'xs
x sin(nπx) dx
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