- 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
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![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]
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