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Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 50/u(t, x), t≤ (0, ∞), x = (0,3); with Neumann boundary conditions du(t,0) = 0 and du(t, 3) = 0 and with initial condition u(0, x) = f(x) = Co = Cn = u(t, x) The solution u of the problem above, with the conventions given in class, has the form = with the normalization conditions v₁ (0) = 1 and wn (0) vn (t) = wn(x) 3, 4, Co 90 +29 2 n= x = 0, x E Cn Un (t) wn(x), = 1. Find the functions Un, wn, and the constants co and cn for n > 1. Σ M M Σ

Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 50/u(t, x), t≤ (0, ∞), x = (0,3); with Neumann boundary conditions du(t,0) = 0 and du(t, 3) = 0 and with initial condition u(0, x) = f(x) = Co = Cn = u(t, x) The solution u of the problem above, with the conventions given in class, has the form = with the normalization conditions v₁ (0) = 1 and wn (0) vn (t) = wn(x) 3, 4, Co 90 +29 2 n= x = 0, x E Cn Un (t) wn(x), = 1. Find the functions Un, wn, and the constants co and cn for n > 1. Σ M M Σ

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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Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 5 du(t, x), t≤ (0, ∞), x = (0,3); with Neumann boundary conditions du(t,0) = 0 and du(t, 3) = 0 and with initial condition u(0, x) = f(x) = Co = Cn = u(t, x) The solution u of the problem above, with the conventions given in class, has the form +29 n= = with the normalization conditions v₁ (0) = 1 and wn (0) vn (t) = wn(x) Co 2 3, 4, x = 0, x E Cn Un (t) wn(x), = 1. Find the functions Un, wn, and the constants co and cn for n > 1. Σ M M Σ
Transcribed Image Text:Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 5 du(t, x), t≤ (0, ∞), x = (0,3); with Neumann boundary conditions du(t,0) = 0 and du(t, 3) = 0 and with initial condition u(0, x) = f(x) = Co = Cn = u(t, x) The solution u of the problem above, with the conventions given in class, has the form +29 n= = with the normalization conditions v₁ (0) = 1 and wn (0) vn (t) = wn(x) Co 2 3, 4, x = 0, x E Cn Un (t) wn(x), = 1. Find the functions Un, wn, and the constants co and cn for n > 1. Σ M M Σ
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