Solve the Boundary-Initial Value Problem where a = n 21 k Remember that has already been factored out! g²u Ju მ2 Ot du da = that models the temperature of a heated wire with insulated ends. The series solution of the boundary value problem is 3 (0, t) = 0, u(a,0)=x², u(x, t) 0 0 du д: 0< a 0 = - ²/2 ²₂e (-+*+¹) cos ( Σ ane 08 72=0 (117) L

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.CR: Chapter 11 Review
Problem 12CR
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Solve the Boundary-Initial Value Problem
where a₁ =
n> 1
k
Remember that has already been factored out!
2²u Ju
მ2 Ət
du
da
=
3
that models the temperature of a heated wire with insulated ends. The series solution of the boundary value problem is
(0, t) = 0,
u(a,0)=x²,
0<a<L, t> 0
du
8x
0 < a <L
(L,t)=0, t>0
u(x, t)
- ²/2 (
Σ ane (-²²¹) cos
08 (117)
=
L
72=0
Transcribed Image Text:Solve the Boundary-Initial Value Problem where a₁ = n> 1 k Remember that has already been factored out! 2²u Ju მ2 Ət du da = 3 that models the temperature of a heated wire with insulated ends. The series solution of the boundary value problem is (0, t) = 0, u(a,0)=x², 0<a<L, t> 0 du 8x 0 < a <L (L,t)=0, t>0 u(x, t) - ²/2 ( Σ ane (-²²¹) cos 08 (117) = L 72=0
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