- Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and À.
- Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and À.
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
![1- Show that u(x,t) = e-at[A sin(x) + B cos(Ax)] satisfies the PDE
U = a²u for arbitrary A, B and A.
2- Show sin(max) sin(nax) dx
m =
%3D
(1/2 m = n
HINT Use the identity
sin(mx) sin(nx) =[cos(m-n)x- cos(m + n)x]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe33c96fa-22c1-4687-8435-061d0614f9de%2Fc8e6fc15-a002-4eba-a345-71cd587d5085%2Fjld05ywr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1- Show that u(x,t) = e-at[A sin(x) + B cos(Ax)] satisfies the PDE
U = a²u for arbitrary A, B and A.
2- Show sin(max) sin(nax) dx
m =
%3D
(1/2 m = n
HINT Use the identity
sin(mx) sin(nx) =[cos(m-n)x- cos(m + n)x]
Expert Solution

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 2 steps with 2 images

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

