The temperature ne-dimensional distribution u(t) along a wire of length L is governed by th heat equation: a a² [u(x, t)]=- [u(x, t)] əx² where ß is a positive constant. olve this equation using the ssumption that the form of the solution is: .)-f(x) u(x, t) = f(x) g(t) wil.
The temperature ne-dimensional distribution u(t) along a wire of length L is governed by th heat equation: a a² [u(x, t)]=- [u(x, t)] əx² where ß is a positive constant. olve this equation using the ssumption that the form of the solution is: .)-f(x) u(x, t) = f(x) g(t) wil.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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![2. The temperature distribution u(t) along a wire of length L is governed by the
one-dimensional heat equation :
a
2²
[u(x, t)]
-Bax² [u(x, t)]
where is a positive constant.
Solve this equation using the
assumption that the form of the solution is:
0,1)=0
sir.0)=f(x)
Onitial temps, distribution)
u(x, t) = f(x) · g(t)
(1.1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F535cb7da-23fd-459f-9f59-a568f8dd366d%2F7907a6f5-6662-4dae-9426-d220d3ddbb5e%2Ff3vntsb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. The temperature distribution u(t) along a wire of length L is governed by the
one-dimensional heat equation :
a
2²
[u(x, t)]
-Bax² [u(x, t)]
where is a positive constant.
Solve this equation using the
assumption that the form of the solution is:
0,1)=0
sir.0)=f(x)
Onitial temps, distribution)
u(x, t) = f(x) · g(t)
(1.1)
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