Solve ut - 2ux = 0, -∞ 0 u(x, 0) = 4 cos(x) First change to characteristic coordinates (§, 8) where s = ξ = help (formulas) = t and picked so that when s = t = 0 then $ = x, and that the equation becomes the ODE us = 0. Solve and write u in terms of (§, s) : u = help (formulas) Finally write u in terms of (x,t): u = ☐ help (formulas) Book: Section 1.9 of Notes on Diffy Qs

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.5: Trigonometric Graphs
Problem 29E
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Solve
ut - 2ux = 0, -∞<x<∞, t> 0
u(x, 0) = 4 cos(x)
First change to characteristic coordinates (§, 8) where s =
ξ
=
help (formulas)
= t and
picked so that when s = t = 0 then $ = x, and that the equation becomes the ODE us = 0.
Solve and write u in terms of (§, s) :
u =
help (formulas)
Finally write u in terms of (x,t):
u =
☐ help (formulas)
Book: Section 1.9 of Notes on Diffy Qs
Transcribed Image Text:Solve ut - 2ux = 0, -∞<x<∞, t> 0 u(x, 0) = 4 cos(x) First change to characteristic coordinates (§, 8) where s = ξ = help (formulas) = t and picked so that when s = t = 0 then $ = x, and that the equation becomes the ODE us = 0. Solve and write u in terms of (§, s) : u = help (formulas) Finally write u in terms of (x,t): u = ☐ help (formulas) Book: Section 1.9 of Notes on Diffy Qs
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