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Let u be the solution to the initial boundary value problem for the Heat Equation, with Mixed boundary conditions au(t,0) = 0 and u(t, 3) with the normalization conditions vn (0) vn (t) = e^((-5(2n-1)^2pi^2/9t)) w₁(x) = cos(((2n-1)pi/2x)/3) Cn = du(t, x) = 5 du(t, x), t= (0,00), x = (0, 3); The solution of the problem above, with the conventions given in class, has the form Ա 8/((2n-1)pi)sin((npi/2)-pi/4) = 0 and with initial condition u(0, x) = f(x) = M M 3, 0, M = 1 and wn (0) = 1. Find the functions un, wn, and the constants C- TE 0, XE [0,2), 12 u(t, x) = cn vn (t) w₁(x), n=1

Let u be the solution to the initial boundary value problem for the Heat Equation, with Mixed boundary conditions au(t,0) = 0 and u(t, 3) with the normalization conditions vn (0) vn (t) = e^((-5(2n-1)^2pi^2/9t)) w₁(x) = cos(((2n-1)pi/2x)/3) Cn = du(t, x) = 5 du(t, x), t= (0,00), x = (0, 3); The solution of the problem above, with the conventions given in class, has the form Ա 8/((2n-1)pi)sin((npi/2)-pi/4) = 0 and with initial condition u(0, x) = f(x) = M M 3, 0, M = 1 and wn (0) = 1. Find the functions un, wn, and the constants C- TE 0, XE [0,2), 12 u(t, x) = cn vn (t) w₁(x), n=1

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, with Mixed boundary conditions au(t,0) = 0 and u(t, 3) with the normalization conditions vn (0) vn (t) = e^((-5(2n-1)^2pi^2/9t)) w₁(x) = cos(((2n-1)pi/2x)/3) Cn = du(t, x) = 5 du(t, x), t= (0,00), x = (0, 3); The solution of the problem above, with the conventions given in class, has the form U 8/((2n-1)pi)sin((npi/2)-pi/4) = 0 and with initial condition u(0, x) = f(x) = M M 3, 0, M = 1 and wn (0) = 1. Find the functions un, wn, and the constants C- TE 0, XE [0,2), 12 u(t, x) = cn vn (t) w₁(x), n=1
Transcribed Image Text:Let u be the solution to the initial boundary value problem for the Heat Equation, with Mixed boundary conditions au(t,0) = 0 and u(t, 3) with the normalization conditions vn (0) vn (t) = e^((-5(2n-1)^2pi^2/9t)) w₁(x) = cos(((2n-1)pi/2x)/3) Cn = du(t, x) = 5 du(t, x), t= (0,00), x = (0, 3); The solution of the problem above, with the conventions given in class, has the form U 8/((2n-1)pi)sin((npi/2)-pi/4) = 0 and with initial condition u(0, x) = f(x) = M M 3, 0, M = 1 and wn (0) = 1. Find the functions un, wn, and the constants C- TE 0, XE [0,2), 12 u(t, x) = cn vn (t) w₁(x), n=1
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