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72. Show that each of the following functions is a solution of the wave equation u₁1 = a²uxx. (a) u = sin(kx) sin(akt) (b) u = t/(a²t² − x²) (c) u = (x - at) + (x + at)6 (d) u = sin(x − at) + ln(x + at)

72. Show that each of the following functions is a solution of the wave equation u₁1 = a²uxx. (a) u = sin(kx) sin(akt) (b) u = t/(a²t² − x²) (c) u = (x - at) + (x + at)6 (d) u = sin(x − at) + ln(x + at)

Advanced Engineering Mathematics
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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72) Show that each of the following functions is a solution of the wave equation  u_tt = a^2u_xx.

72. Show that each of the following functions is a solution of the wave equation u₁ = a²uxx. (a) u = sin(kx) sin(akt) (b) u = t/(a²t² = t/(a²t² - x²) (c) u = (xat) + (x + at)6 (d) u = sin(xat) + In(x + at)
Transcribed Image Text:72. Show that each of the following functions is a solution of the wave equation u₁ = a²uxx. (a) u = sin(kx) sin(akt) (b) u = t/(a²t² = t/(a²t² - x²) (c) u = (xat) + (x + at)6 (d) u = sin(xat) + In(x + at)
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