Question 4 (a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation U₁ = Uxx, x > 0. (b) Consider the solution U(x,t) = (sin x)et of the heat equation U₁ = Uxx. Find the location of its maxima and minima in the rectangle πT {0≤ x ≤½,0≤ t≤T} 2' (c) Solve the following heat equation with boundary and initial condition on the half line {x>0} (explain your reasonings for every steps). Ut = Uxx, x > 0 Ux(0,t) = 0 U(x, 0) = = =1 [4] [6] [10]
Question 4 (a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation U₁ = Uxx, x > 0. (b) Consider the solution U(x,t) = (sin x)et of the heat equation U₁ = Uxx. Find the location of its maxima and minima in the rectangle πT {0≤ x ≤½,0≤ t≤T} 2' (c) Solve the following heat equation with boundary and initial condition on the half line {x>0} (explain your reasonings for every steps). Ut = Uxx, x > 0 Ux(0,t) = 0 U(x, 0) = = =1 [4] [6] [10]
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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![Question 4
(a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation
U₁ = Uxx, x > 0.
(b) Consider the solution U(x,t) = (sin x)et of the heat equation U₁ = Uxx. Find the
location of its maxima and minima in the rectangle
πT
{0≤ x ≤½,0≤ t≤T}
2'
(c) Solve the following heat equation with boundary and initial condition on the half
line {x>0} (explain your reasonings for every steps).
Ut
=
Uxx, x > 0
Ux(0,t) = 0
U(x, 0) =
= =1
[4]
[6]
[10]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab10482b-5b4c-4b70-8917-22b03124ed98%2F160bc263-4f36-41ea-9a67-262ed18ba7c8%2Fisbbtl8_processed.png&w=3840&q=75)
Transcribed Image Text:Question 4
(a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation
U₁ = Uxx, x > 0.
(b) Consider the solution U(x,t) = (sin x)et of the heat equation U₁ = Uxx. Find the
location of its maxima and minima in the rectangle
πT
{0≤ x ≤½,0≤ t≤T}
2'
(c) Solve the following heat equation with boundary and initial condition on the half
line {x>0} (explain your reasonings for every steps).
Ut
=
Uxx, x > 0
Ux(0,t) = 0
U(x, 0) =
= =1
[4]
[6]
[10]
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