Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the following boundary-value problem : = 0, 0<1< 1,y>0 (1) u(0, 3) = 0 and u(1,3) = 0, y>0, (2) (L) u(r, y) → 0, as y → +∞ (3) u(z,0) = 1 0

Consider the following boundary-value problem : = 0, 0<1< 1,y>0 (1) u(0, 3) = 0 and u(1,3) = 0, y>0, (2) (L) u(r, y) → 0, as y → +∞ (3) u(z,0) = 1 0

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
fpde
Consider the following boundary-value problem : u u = 0, 0<r< 1,y > 0 (1) u(0, у) — 0 and и(1, у) — 0, у> 0, (2) (L) %3D u(r, y) → 0, as y → +o (3) u(x,0) = 1 0<a<1 (4) (1) By using the method of separation of variables, the family of solutions un(r, y) for equations (1), (2) and (3) is a. Un(r, y) = Bne-nEY sin(na2) b. Un(r, y) = Bne¯n=Y cos(nTr) %3D c. Un(x, y) = Bne cos(nTy) d. None of the above +00 (2) Let u(x, y = D„(1,y) be a solution of (L). By using the initial condition (4), we obtain that a. Ban+1 = 0 and Ban b. B2n = 0 and Ben+1 = (2n+1) 8. с. Ва (2n +1)2n d. None of the above
Transcribed Image Text:Consider the following boundary-value problem : u u = 0, 0<r< 1,y > 0 (1) u(0, у) — 0 and и(1, у) — 0, у> 0, (2) (L) %3D u(r, y) → 0, as y → +o (3) u(x,0) = 1 0<a<1 (4) (1) By using the method of separation of variables, the family of solutions un(r, y) for equations (1), (2) and (3) is a. Un(r, y) = Bne-nEY sin(na2) b. Un(r, y) = Bne¯n=Y cos(nTr) %3D c. Un(x, y) = Bne cos(nTy) d. None of the above +00 (2) Let u(x, y = D„(1,y) be a solution of (L). By using the initial condition (4), we obtain that a. Ban+1 = 0 and Ban b. B2n = 0 and Ben+1 = (2n+1) 8. с. Ва (2n +1)2n d. None of the above
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

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