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Consider the Boundary-Initial Value problem J²u и ди 4 0 < x < 6, t> 0 მე2 It u(0,t) = 0, 0, u(6,t) = 0, t>0 u(x, 0) = x(6x), 0 < x <6 This models a heated wire, with zero endpoints temperatures. The solution u(x,t) of the initial-boundary value problem is given by the series u(x,t)-b, sin П3 n=1 (b, sin ((2n − 1) — x) e-cnt where bn ☐ and Сп ☐

Consider the Boundary-Initial Value problem J²u и ди 4 0 < x < 6, t> 0 მე2 It u(0,t) = 0, 0, u(6,t) = 0, t>0 u(x, 0) = x(6x), 0 < x <6 This models a heated wire, with zero endpoints temperatures. The solution u(x,t) of the initial-boundary value problem is given by the series u(x,t)-b, sin П3 n=1 (b, sin ((2n − 1) — x) e-cnt where bn ☐ and Сп ☐

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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Consider the Boundary-Initial Value problem J²u и ди 4 0 < x < 6, t> 0 მე2 It u(0,t) = 0, 0, u(6,t) = 0, t>0 u(x, 0) = x(6x), 0 < x <6 This models a heated wire, with zero endpoints temperatures. The solution u(x,t) of the initial-boundary value problem is given by the series u(x,t)-b, sin П3 n=1 (b, sin ((2n − 1) — x) e-cnt where bn ☐ and Сп ☐
Transcribed Image Text:Consider the Boundary-Initial Value problem J²u и ди 4 0 < x < 6, t> 0 მე2 It u(0,t) = 0, 0, u(6,t) = 0, t>0 u(x, 0) = x(6x), 0 < x <6 This models a heated wire, with zero endpoints temperatures. The solution u(x,t) of the initial-boundary value problem is given by the series u(x,t)-b, sin П3 n=1 (b, sin ((2n − 1) — x) e-cnt where bn ☐ and Сп ☐
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