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Let u = (x,t) represent the temperature of a hose with length L. The temperature with t= 0 is u(x,0) = x/L (1-(x/L)) 0<=x<=L temperature at the hose-ends is constnat u(0,t) = u(L,t) = 0    t>0 t inside the hose differs by the equation ut = α2uxx  , 00            α = constant use method with seperation of variables to determine u = u(x,t) when t>0

Let u = (x,t) represent the temperature of a hose with length L. The temperature with t= 0 is u(x,0) = x/L (1-(x/L)) 0<=x<=L temperature at the hose-ends is constnat u(0,t) = u(L,t) = 0    t>0 t inside the hose differs by the equation ut = α2uxx  , 00            α = constant use method with seperation of variables to determine u = u(x,t) when t>0

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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Let u = (x,t) represent the temperature of a hose with length L. The temperature with t= 0 is u(x,0) = x/L (1-(x/L))

0<=x<=L

temperature at the hose-ends is constnat u(0,t) = u(L,t) = 0    t>0
t inside the hose differs by the equation ut = α2uxx  , 0<x<L     t>0            α = constant

use method with seperation of variables to determine u = u(x,t) when t>0

 

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