Solve the Boundary-Initial Value Problem du Ət k d²u Əx² = du dx u(x,0) = x², > ·(0, t) = 0, where an = du dx 00 ∞ 2 L u(x, t) ane (-²¹) cos (172) (2² = L n=0 -(L,t) = 0, t>0 n> 1 Remember that has already been factored out! 2 L

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 9T
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Solve the Boundary-Initial Value Problem
du
Ət
k
² u
Əx²
=
Ju
əx
u(x,0) = x²,
(0, t) = 0,
2
where an =
that models the temperature of a heated wire with
insulated ends. The series solution of the boundary
value problem is
2
0 < x < L, t> 0
ди
əx
0<x<L
u(x, t) Σane (-***) cos
=
n=0
(L,t)=0, t>0
n> 1
NTT
X
Remember that has already been factored out!
L
Transcribed Image Text:Solve the Boundary-Initial Value Problem du Ət k ² u Əx² = Ju əx u(x,0) = x², (0, t) = 0, 2 where an = that models the temperature of a heated wire with insulated ends. The series solution of the boundary value problem is 2 0 < x < L, t> 0 ди əx 0<x<L u(x, t) Σane (-***) cos = n=0 (L,t)=0, t>0 n> 1 NTT X Remember that has already been factored out! L
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