Homework Help is Here – Start Your Trial Now!
Math
Calculus
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
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...
See similar textbooks
icon
Related questions
Question

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
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
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS