If(x) = -²X(z), what is the ODE obeyed by T(t)? [use T to indicate T(t)] Which of the following solutions obey the boundary conditions X(0) = 0 and (L) = 0? [tick all that are correct-points will be deducted for wro answers] □ sin() □sin() sin() for k integer □sin(²) □sin(37) sin(. -) for k integer (2k+1)az 2L Which of the following is a possible solution of the above wave equation? ○ cos(kz)e-ket cos(kcz) sin(kt) O Ar + B ○ cos(kx) sin(kt) O None of the choices apply
If(x) = -²X(z), what is the ODE obeyed by T(t)? [use T to indicate T(t)] Which of the following solutions obey the boundary conditions X(0) = 0 and (L) = 0? [tick all that are correct-points will be deducted for wro answers] □ sin() □sin() sin() for k integer □sin(²) □sin(37) sin(. -) for k integer (2k+1)az 2L Which of the following is a possible solution of the above wave equation? ○ cos(kz)e-ket cos(kcz) sin(kt) O Ar + B ○ cos(kx) sin(kt) O None of the choices apply
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
![This question tests understanding of separation of variables as applied to PDES.
The wave equation
may be studied by separation of variables: u(x, t) = X(x)T(t).
If (x) = −k²X(x), what is the ODE obeyed by T(t)? [use T to indicate T(t)]
d²T_
de²
Which of the following solutions obey the boundary conditions X(0) = 0 and (L) = 0? [tick all that are correct-points will be deducted for wrong
answers]
□sin(7)
sin(7)
□sin(**) for k integer
sin(²)
□sin (³) sin(
(2k+1)az.
2L
for k integer
Which of the following is a possible solution of the above wave equation?
○ cos(kx)e-ket O cos(kcz)sin(kt) O Az + B ○ cos(kx) sin(kt) O None of the choices apply
[D/HD] Which of the following PDEs cannot be solved exactly by using the separation of variables u(x, y) = X(x)Y(y)) where we attain different ODES
for X(x) and Y(y)?
=
-u] = Qu
=Q[+e="]
Q[+u]
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53ce1657-b18a-4e5a-99aa-3e87bdade9e3%2F48ba4b85-ceee-4847-b9d3-6cec106f311e%2Fib2cihd_processed.png&w=3840&q=75)
Transcribed Image Text:This question tests understanding of separation of variables as applied to PDES.
The wave equation
may be studied by separation of variables: u(x, t) = X(x)T(t).
If (x) = −k²X(x), what is the ODE obeyed by T(t)? [use T to indicate T(t)]
d²T_
de²
Which of the following solutions obey the boundary conditions X(0) = 0 and (L) = 0? [tick all that are correct-points will be deducted for wrong
answers]
□sin(7)
sin(7)
□sin(**) for k integer
sin(²)
□sin (³) sin(
(2k+1)az.
2L
for k integer
Which of the following is a possible solution of the above wave equation?
○ cos(kx)e-ket O cos(kcz)sin(kt) O Az + B ○ cos(kx) sin(kt) O None of the choices apply
[D/HD] Which of the following PDEs cannot be solved exactly by using the separation of variables u(x, y) = X(x)Y(y)) where we attain different ODES
for X(x) and Y(y)?
=
-u] = Qu
=Q[+e="]
Q[+u]
0
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