Problem 6: The one-dimensional diffusion equation is given by: ди m at a2u Show that the following are solutions to the diffusion equation. (a) u = A exp +B, where A and B are constants. (b) u=A exp(-ax) cos(ax - 2ma?t +B)+C, where A, B, C, and a are constants.
Problem 6: The one-dimensional diffusion equation is given by: ди m at a2u Show that the following are solutions to the diffusion equation. (a) u = A exp +B, where A and B are constants. (b) u=A exp(-ax) cos(ax - 2ma?t +B)+C, where A, B, C, and a are constants.
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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![Problem 6:
The one-dimensional diffusion equation is given by:
ди
a2u
at
Show that the following are solutions to the diffusion equation.
(а) и
Aexp
+B, where A and B are constants.
(b) u=A exp(-ax) cos(ax - 2ma?t +B)+C, where A, B, C, and a are constants.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2acb2dd0-e296-48e2-b898-fcb8815b7566%2Fddcaa97b-f8a7-403b-89b2-7a9f9568beae%2Fli9cptd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 6:
The one-dimensional diffusion equation is given by:
ди
a2u
at
Show that the following are solutions to the diffusion equation.
(а) и
Aexp
+B, where A and B are constants.
(b) u=A exp(-ax) cos(ax - 2ma?t +B)+C, where A, B, C, and a are constants.
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