x and time t of a particular heat equation is: U(x,t) = [Cn(e-6tn^2)sin(nx) where the sum goes from 1 to ∞. A) Write out the heat equation that has this solution including the boundary conditions. B) If U(x,0) = 3sin(2x) -5sin(4x) find the two non-zero coefficients Cn C) Find U(x,t).
x and time t of a particular heat equation is: U(x,t) = [Cn(e-6tn^2)sin(nx) where the sum goes from 1 to ∞. A) Write out the heat equation that has this solution including the boundary conditions. B) If U(x,0) = 3sin(2x) -5sin(4x) find the two non-zero coefficients Cn C) Find U(x,t).
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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Transcribed Image Text:A general solution for the temperature, U, as a function of position
x and time t of a particular heat equation is:
U(x,t) = [Cn(e-6tn^2)sin(nx) where the sum goes
from 1 to ∞.
A) Write out the heat equation that has this solution
including the boundary conditions.
B) If U(x,0) = 3sin(2x) -5sin(4x) find the two non-zero
coefficients Cn
C) Find U(x,t).
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