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Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

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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(a) Show that the function y(x, t) = x2 + v²t is a solution to the wave equation, by calculating the following quantities and expressing each in terms of x, v, and t. dy/at = dy/dx = (a?y/ar?)/v2 = y/ax? = (b) Show that the function in part (a) can be written as f(x + vt) + g(x - vt), and determine the functional forms for f and g. f(x + vt) = g(x- vt) = (c) Repeat parts (a) and (b) for the function y(x, t) = sin (x) cos (vt). dy/at = dy/dx = %3D azy/ax? = f(x + vt) = g(x- vt) =
Transcribed Image Text:(a) Show that the function y(x, t) = x2 + v²t is a solution to the wave equation, by calculating the following quantities and expressing each in terms of x, v, and t. dy/at = dy/dx = (a?y/ar?)/v2 = y/ax? = (b) Show that the function in part (a) can be written as f(x + vt) + g(x - vt), and determine the functional forms for f and g. f(x + vt) = g(x- vt) = (c) Repeat parts (a) and (b) for the function y(x, t) = sin (x) cos (vt). dy/at = dy/dx = %3D azy/ax? = f(x + vt) = g(x- vt) =
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