(b) Solve the first equation for u in terms of v as u(x, 1) = f' t) v(x − ct +cs, s) ds.
(b) Solve the first equation for u in terms of v as u(x, 1) = f' t) v(x − ct +cs, s) ds.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
[Second Order Equations] How do you solve 6b?
Transcribed Image Text:6. Derive the formula for the inhomogeneous wave equation in yet another
way.
(a) Write it as the system
Ut + cux = V, Ut - CVx = f.
(b) Solve the first equation for u in terms of v as
t
= S'
u(x, t)
v(x − ct + cs, s) ds.
(c) Similarly, solve the second equation for v in terms of f.
(d) Substitute part (c) into part (b) and write as an iterated integral.
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