Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the partial differential equation du at' du (0, t) = 0 and u(37, t) = 0 for t > 0. with boundary conditions Applying the method of separation of variables with u(x, t) = X(x)T(t) gives the ordinary differential equations X" = µX, T = µT,

Consider the partial differential equation du at' du (0, t) = 0 and u(37, t) = 0 for t > 0. with boundary conditions Applying the method of separation of variables with u(x, t) = X(x)T(t) gives the ordinary differential equations X" = µX, T = µT,

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%

q8

Consider the partial differential equation du with boundary conditions (0, t) = 0 and u(37, t) = 0 for t > 0. Applying the method of separation of variables with u(x, t) = X(x)T(t) gives the ordinary differential equations x" = µX, T = µT, where u is a non-zero separation constant. You may assume that u = -k?, where k is a positive constant. Select the option that gives a family of non-trivial solutions for u(x, t) that satisfy the partial differential equation and boundary conditions. Select one: Un (T, t) = An sin(ka) e¬k*, where k = : and n = 1,2,... Un (x, t) = An sin(kæ) ekt, where k = - and n = 1, 2,... 6. Un (x, t) = An cos(kæ) e¬*t, where k = ? and n = 1,2,... 3 Un (x, t) = = An sin(ka) eki, where k = ? and n = 1, 2,... Un (x, t) = An cos(ka) ekt, where k = - and n = 1, 2, ... 3
Transcribed Image Text:Consider the partial differential equation du with boundary conditions (0, t) = 0 and u(37, t) = 0 for t > 0. Applying the method of separation of variables with u(x, t) = X(x)T(t) gives the ordinary differential equations x" = µX, T = µT, where u is a non-zero separation constant. You may assume that u = -k?, where k is a positive constant. Select the option that gives a family of non-trivial solutions for u(x, t) that satisfy the partial differential equation and boundary conditions. Select one: Un (T, t) = An sin(ka) e¬k*, where k = : and n = 1,2,... Un (x, t) = An sin(kæ) ekt, where k = - and n = 1, 2,... 6. Un (x, t) = An cos(kæ) e¬*t, where k = ? and n = 1,2,... 3 Un (x, t) = = An sin(ka) eki, where k = ? and n = 1, 2,... Un (x, t) = An cos(ka) ekt, where k = - and n = 1, 2, ... 3
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS