Show that each of the following two functions is a solution of the heat equation ĉuļət = k² a²u/ax² (k a constant). (a) e-k²a²t sin ax. (b)(1/√t) exp(-x²/4k²t).
Show that each of the following two functions is a solution of the heat equation ĉuļət = k² a²u/ax² (k a constant). (a) e-k²a²t sin ax. (b)(1/√t) exp(-x²/4k²t).
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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Transcribed Image Text:Show that each of the following two functions is a solution of the heat equation du/dt =
k² ô²u/əx² (k a constant).
- k2a2t
(a) e
sin ax.
(b) (1/√t) exp(-x²/4k²t).
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