Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
ди dt 00 dx2 ди u(0, г) — 0 %3DИо, %3D -h (u (1,1) — ио), һ>0, t>0 and u(x, 0) %3D f(x), 0

ди dt 00 dx2 ди u(0, г) — 0 %3DИо, %3D -h (u (1,1) — ио), һ>0, t>0 and u(x, 0) %3D f(x), 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

How come lambda=0 and lambda=a^2 don't satisfy the boundary conditions. Can you please explain it to me. Thank you 

6:29 PM Sat May 1 * 12% AA bartleby.com Bb Sign i Bb What if I add... Sign in Bb Request AA... Sign in Answered: P... = bartleby Q Search for textbooks, step-by-step explanatio... Ask an Expert Math / Advanced Math / Q&A Library | Please find attached the question as you told me to upload.l don't understand w... Please find attached the question as you told me to upload.I don't understand why tan(a... u (0, t) = 0, , = -h (u (1, t) – uo), h> 0,1 > 0 and u (x, 0) = f (x), 0 <x < 1. X GET 10 FREE QUESTIONS Expert Answer Step 1 Given boundary value problem is kPu dx 2 ди 0<x<1, t>0 dt > ди u(0, t) = 0 = uo, ax :-h (u (1, t) – uo), h>0, t>0 and u(x, 0) = f(x), 0<x<1. x=1 We will solve this by variable separation method. Let u(x, t) = X(x)T(t) is the solution of the given boundary value problem, 1 d² x X dx2 d² x 1 dT then kT- d x2 dt kT dt a (positive), we are not able to get any solution which satisfy all the boundary conditions. -a° (negative). For 2 = 0 and 1 So, we can neglect these conditions. Now let 1 %3| 7²kt Then by above equation we get, X А cos (аx) + B sin (аx) and T — Се а'ki. Hence, u (x, t) = [A cos (ax) + B sin (ax)] (Ce-a*ki) ...(1) Step 2 Since, u(0, t) = 0. So, by (1), we get
Transcribed Image Text:6:29 PM Sat May 1 * 12% AA bartleby.com Bb Sign i Bb What if I add... Sign in Bb Request AA... Sign in Answered: P... = bartleby Q Search for textbooks, step-by-step explanatio... Ask an Expert Math / Advanced Math / Q&A Library | Please find attached the question as you told me to upload.l don't understand w... Please find attached the question as you told me to upload.I don't understand why tan(a... u (0, t) = 0, , = -h (u (1, t) – uo), h> 0,1 > 0 and u (x, 0) = f (x), 0 <x < 1. X GET 10 FREE QUESTIONS Expert Answer Step 1 Given boundary value problem is kPu dx 2 ди 0<x<1, t>0 dt > ди u(0, t) = 0 = uo, ax :-h (u (1, t) – uo), h>0, t>0 and u(x, 0) = f(x), 0<x<1. x=1 We will solve this by variable separation method. Let u(x, t) = X(x)T(t) is the solution of the given boundary value problem, 1 d² x X dx2 d² x 1 dT then kT- d x2 dt kT dt a (positive), we are not able to get any solution which satisfy all the boundary conditions. -a° (negative). For 2 = 0 and 1 So, we can neglect these conditions. Now let 1 %3| 7²kt Then by above equation we get, X А cos (аx) + B sin (аx) and T — Се а'ki. Hence, u (x, t) = [A cos (ax) + B sin (ax)] (Ce-a*ki) ...(1) Step 2 Since, u(0, t) = 0. So, by (1), we get
Expert Solution
steps

Step by step

Solved in 6 steps with 7 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Inequality
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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