Part 3. Use separation of variables to obtain a product solution to the following: dud?u + əx² ay² 1. to be the form of the solution u? A. u = X(x)T(t) B. u = xt C. u = X(x)Y(y) D. u = xy 2 A. B. Using the method of separation of variables, which of the following is assumed = 0 Which of the following can be obtained after substitution of your answer in (1)? Y" X=-7 == Y VII VII
Part 3. Use separation of variables to obtain a product solution to the following: dud?u + əx² ay² 1. to be the form of the solution u? A. u = X(x)T(t) B. u = xt C. u = X(x)Y(y) D. u = xy 2 A. B. Using the method of separation of variables, which of the following is assumed = 0 Which of the following can be obtained after substitution of your answer in (1)? Y" X=-7 == Y VII VII
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Answer 6 Only Part 3
Transcribed Image Text:Part 3. Use separation of variables to obtain a product solution to the following:
²ud²u
+
əx² ay²
1.
to be the form of the solution u?
A. u = X(x)T(t)
B. u = xt
C. u = X(x)Y(y)
D. u = xy
2
A.
B.
C.
D.
3.
Using the method of separation of variables, which of the following is assumed
Which of the following can be obtained after substitution of your answer in (1)?
X"
reduced into
A. Two first-order ODES
B. Two second-order ODES
= 0
X" Y"
Y
X
=
Y"
Y
Y'
X=Y
C. A first-order ODE and a second-order ODE
D. None of these
From the correct answer in (2), the given partial differential equation can be
Y"
Y
Transcribed Image Text:4
A. 1
B. 2
C. 3
D. 4
If the correct answer in (2) is equal to -, how many case/s is/are possible?
5
Using the correct answers in (2) and (4), if λ = -a², the solution is
A. u = (A₁ cosh ax + A₂ sinh ax)(B₁ cos ay + B₂ sin ay)
B. u = (A₁ cos ax + A₂ sin ax) (B₁ cosh ay + B₂ sinh ay)
C. u = (A1 cosh ax + A, sinh ax)(Bị cosh ay + B2 sinhay)
D. u = (A₁ cos ax + A₂ sin ax) (B₁ cos ay + B₂ sin ay)
Using the correct answers in (2) and (4), if λ = 0, the solution is
6
A. u A3x + A4Y
B. u= (A3 + A4x) (B3 + B4Y)
C. u= A3 + A4x
D. u A3 + A4y
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