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Problem 3: Let u = u(x, t), −2 ≤ x ≤ 3 and t ≥ 1. Using a suitable change of variables, write the problem ut(x, t) = 5Uxx (x, t), u(2, 1) = sin(Tr), [u(-2, t) = u(3, t) = 0, -2 < x <3, t > 1, -2 ≤ x ≤ 3, t≥ 1. in the form v(x, t) = u(ax+b, ct+d), where a, b, c, d are constants, so that v is a solution to the problem (v₁(x, t) = Vxx (x, t), 0 < x < L, t > 0, 0≤x≤L, v(x,0) = y(x), ¸v(0, t) = v(L, t) =0, t≥0. Give the other parameters and as functions of L.

Problem 3: Let u = u(x, t), −2 ≤ x ≤ 3 and t ≥ 1. Using a suitable change of variables, write the problem ut(x, t) = 5Uxx (x, t), u(2, 1) = sin(Tr), [u(-2, t) = u(3, t) = 0, -2 < x <3, t > 1, -2 ≤ x ≤ 3, t≥ 1. in the form v(x, t) = u(ax+b, ct+d), where a, b, c, d are constants, so that v is a solution to the problem (v₁(x, t) = Vxx (x, t), 0 < x < L, t > 0, 0≤x≤L, v(x,0) = y(x), ¸v(0, t) = v(L, t) =0, t≥0. Give the other parameters and as functions of L.

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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Problem 3: Let u variables, write the problem = u(x, t), −2 ≤ x ≤ 3 and t ≥ 1. Using a suitable change of [ut(x, t) = 5Uxx (x, t), u(x, 1) = sin(x), u(−2, t) = u(3, t)=0, -2 < x <3, t > 1, −2 ≤ x ≤ 3, t≥1. in the form v(x, t) = u(ax+b, ct+d), where a, b, c, d are constants, so that u is a solution to the problem v₁(x, t) = Vxx (x, t), v(x,0) = y(x), 0< x <L,t> 0, 0 ≤ x ≤ L, v(0, t) = v(L, t) =0, t≥0. Give the other parameters and as functions of L.
Transcribed Image Text:Problem 3: Let u variables, write the problem = u(x, t), −2 ≤ x ≤ 3 and t ≥ 1. Using a suitable change of [ut(x, t) = 5Uxx (x, t), u(x, 1) = sin(x), u(−2, t) = u(3, t)=0, -2 < x <3, t > 1, −2 ≤ x ≤ 3, t≥1. in the form v(x, t) = u(ax+b, ct+d), where a, b, c, d are constants, so that u is a solution to the problem v₁(x, t) = Vxx (x, t), v(x,0) = y(x), 0< x <L,t> 0, 0 ≤ x ≤ L, v(0, t) = v(L, t) =0, t≥0. Give the other parameters and as functions of L.
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