Question 4. Consider the equation и, — ихх — их —D 0, 0 < x < 1, t > 0 u(0, 1) %3D 0, и(1,г) %3 1, t > 0, и(х, 0) 3 0, 0
Question 4. Consider the equation и, — ихх — их —D 0, 0 < x < 1, t > 0 u(0, 1) %3D 0, и(1,г) %3 1, t > 0, и(х, 0) 3 0, 0
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
please answer a
![Question 4. Consider the equation
И, — ихх — их — 0,
0 < x < 1, t > 0
u(0, г) %3D 0, и(1,г) —D 1, 1>0,
и(х, 0) — 0, 0 <x<л.
(a)
Consider the change of coordinates u(x,t) = v(x,t)eax+bt¸ and choose a, b to reduce
the equation to a standard heat equation.
(b)
Solve the corresponding equation for v(x,1) using the Fourier series.
Remark. You may use the following statement without proof: the solution to the ODE
y'(t) + ay(t) = f(t)
is
y(t) = e a' y(0) + e af | eas f(s)ds.
-at](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2397270-c13f-4cbc-8085-ef9e58d3496f%2F5e49f9cc-5064-4251-98f1-291ccfbcbd17%2Fbni7zkk_processed.png&w=3840&q=75)
Transcribed Image Text:Question 4. Consider the equation
И, — ихх — их — 0,
0 < x < 1, t > 0
u(0, г) %3D 0, и(1,г) —D 1, 1>0,
и(х, 0) — 0, 0 <x<л.
(a)
Consider the change of coordinates u(x,t) = v(x,t)eax+bt¸ and choose a, b to reduce
the equation to a standard heat equation.
(b)
Solve the corresponding equation for v(x,1) using the Fourier series.
Remark. You may use the following statement without proof: the solution to the ODE
y'(t) + ay(t) = f(t)
is
y(t) = e a' y(0) + e af | eas f(s)ds.
-at
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
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](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)