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Solve Ut 2ux + 9u = 0, -x< x < ∞, t> 0 u(x, 0) = 7 cos(x) First change to characteristic coordinates (§, s) where s = t and ξ = help (formulas) picked so that when s Us + - = t = 0 then § = x, and that the equation becomes an ODE in s : 0 help (formulas) Now write u in terms of (ε, s): u = ☐ help (formulas) Finally write u in terms of (x, t) : u = help (formulas) Book: Section 1.9 of Notes on Diffy Qs

Solve Ut 2ux + 9u = 0, -x< x < ∞, t> 0 u(x, 0) = 7 cos(x) First change to characteristic coordinates (§, s) where s = t and ξ = help (formulas) picked so that when s Us + - = t = 0 then § = x, and that the equation becomes an ODE in s : 0 help (formulas) Now write u in terms of (ε, s): u = ☐ help (formulas) Finally write u in terms of (x, t) : u = help (formulas) Book: Section 1.9 of Notes on Diffy Qs

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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Solve Ut 2ux + 9u = 0, -x< x < ∞, t> 0 u(x, 0) = 7 cos(x) First change to characteristic coordinates (§, s) where s = t and ξ = help (formulas) picked so that when s Us + - = t = 0 then § = x, and that the equation becomes an ODE in s : 0 help (formulas) Now write u in terms of (ε, 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 + 9u = 0, -x< x < ∞, t> 0 u(x, 0) = 7 cos(x) First change to characteristic coordinates (§, s) where s = t and ξ = help (formulas) picked so that when s Us + - = t = 0 then § = x, and that the equation becomes an ODE in s : 0 help (formulas) Now write u in terms of (ε, 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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