his question tests he wave equation may be studied by separation of variables: u(x, t) = X(x)T(t). (a)-k² X(2), what is the ODE obeyed by T(t)? T- Which of the following solutions obey the boundary conditions X(0) = 0 and X (L) = 0? [tick all that are correct-points will be deducted for wrong enswers] (2k+1) m sin( ) for k integer sin(3) □sin() □ sin(2) sin() for k integer sin() 2L don of variables as applied to
his question tests he wave equation may be studied by separation of variables: u(x, t) = X(x)T(t). (a)-k² X(2), what is the ODE obeyed by T(t)? T- Which of the following solutions obey the boundary conditions X(0) = 0 and X (L) = 0? [tick all that are correct-points will be deducted for wrong enswers] (2k+1) m sin( ) for k integer sin(3) □sin() □ sin(2) sin() for k integer sin() 2L don of variables as applied to
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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![This question tests understanding of separation of variables as applied to PDEs.
The wave equation
1,0³
=
may be studied by separation of variables: u(x, t) = X(x)T(t).
If(x) = -k² X(a), what is the ODE obeyed by T(t)?[]
ᏯᎢ .
dt²
Which of the following solutions obey the boundary conditions X(0) = 0 and X (L) = 0? [tick all that are correct-points will be deducted for wrong
answers]
(2k+1) ma
2L
□sin(3)
for k integer
□sin() □ sin(2)
sin(
sin() for k integer
□sin()](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F356f7170-0aa9-429d-a76c-eee9f02e4304%2Ff049b6cf-5822-4bb3-9252-0fac4e31821a%2Fqkb3794_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This question tests understanding of separation of variables as applied to PDEs.
The wave equation
1,0³
=
may be studied by separation of variables: u(x, t) = X(x)T(t).
If(x) = -k² X(a), what is the ODE obeyed by T(t)?[]
ᏯᎢ .
dt²
Which of the following solutions obey the boundary conditions X(0) = 0 and X (L) = 0? [tick all that are correct-points will be deducted for wrong
answers]
(2k+1) ma
2L
□sin(3)
for k integer
□sin() □ sin(2)
sin(
sin() for k integer
□sin()
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