(rux + X(a,b)x)x - Byt = 0, x ]0, 1[, t > 0, Ytt - (x + X(a,b) Ytx)r + Buy = 0, x €]0, 1[, t > 0, u(0, t) = u(1, t) = y(0, t) = y(1, t) = 0, t > 0, u(x,0) = u₁(x), y(x,0) = yo(x), x ≤]0, 1[ u₁(x,0) = u₁(x), y(x,0) = y₁(x), x €]0, 1[, - where r, 3 are positive constants and 0 < a < b <1 1. Find the energy E(t) of the system.
(rux + X(a,b)x)x - Byt = 0, x ]0, 1[, t > 0, Ytt - (x + X(a,b) Ytx)r + Buy = 0, x €]0, 1[, t > 0, u(0, t) = u(1, t) = y(0, t) = y(1, t) = 0, t > 0, u(x,0) = u₁(x), y(x,0) = yo(x), x ≤]0, 1[ u₁(x,0) = u₁(x), y(x,0) = y₁(x), x €]0, 1[, - where r, 3 are positive constants and 0 < a < b <1 1. Find the energy E(t) of the system.
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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Please solve
![Utt-
(rux + X(a,b) Utx)x - Byt = 0, x ]0, 1[, t > 0,
Ytt (yx + X(a,b) Ytx)x+ But = 0, x €]0, 1[, t > 0,
u(0, t) = u(1, t) = y(0, t) = y(1, t) = 0, t > 0,
u(x,0) = u(x), y(x,0) = yo(x), x ≤]0, 1[
ut (x, 0) = u₁(x), yt(x, 0) = y₁(x), x €]0, 1[,
where r, 3 are positive constants and 0 < a < b < 1
1. Find the energy E(t) of the system.
(1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9612a6a5-e19c-4346-ae6e-6941d4a9f0e7%2Fe7f5e07b-8a7f-40e4-a9ed-b0eefd96e22a%2Feqr6jj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Utt-
(rux + X(a,b) Utx)x - Byt = 0, x ]0, 1[, t > 0,
Ytt (yx + X(a,b) Ytx)x+ But = 0, x €]0, 1[, t > 0,
u(0, t) = u(1, t) = y(0, t) = y(1, t) = 0, t > 0,
u(x,0) = u(x), y(x,0) = yo(x), x ≤]0, 1[
ut (x, 0) = u₁(x), yt(x, 0) = y₁(x), x €]0, 1[,
where r, 3 are positive constants and 0 < a < b < 1
1. Find the energy E(t) of the system.
(1)
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