Show that each of the following functions is a solution of the wave equation u t t a 2 u xx (a) u sin(kx) sin(akt) (b) u t (a 2 t 2 x 2 ) (c) u (x at) 6 (x at) 6 (d) u sin(x at) ln(x at) ...

a u sinkx sinakt ut ak sinkx cosakt utt c U k sinkx ...

Show that each of the following functions is a solution of the wave equation u t t

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Show that each of the following functions is a solution of the wave equation u_{t t} = a²u_xx.
(a) u = sin(kx) sin(akt)

(b) u = t/(a²t² - x²)
(c) u = (x - at)⁶ + (x + at)⁶
(d) u = sin(x - at) + ln(x + at)

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Calculus Early Transcendentals

ISBN: 978-1285741550

8th edition

Authors: James Stewart

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Show that each of the following functions is a solution of the wave equation u t t

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Calculus Early Transcendentals

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