u(0, t) = 100, u(1, t) = 100, f(x) = 50 x(1-x), L = 1, c = 1. An= , and bn = f(f(x) - (6) (7) (8) u₁(x) T₂-T₁ L +x+T₁)) sin x dx. Nonzero Boundary Conditions Consider the heat boundary value problem 0 < x 0, u(0, t) = T₁ and u(L, t) = T2, t> 0, u(x,0)=f(x), 0
u(0, t) = 100, u(1, t) = 100, f(x) = 50 x(1-x), L = 1, c = 1. An= , and bn = f(f(x) - (6) (7) (8) u₁(x) T₂-T₁ L +x+T₁)) sin x dx. Nonzero Boundary Conditions Consider the heat boundary value problem 0 < x 0, u(0, t) = T₁ and u(L, t) = T2, t> 0, u(x,0)=f(x), 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
so the question is that left hand picture #12
a couple things, I said "1D wave equation" i meant 1D heat equation
( note that T1= u(0,t)=100 and T2=u(1,t)=100 )
Thank you!
Transcribed Image Text:please solve this 1D wave equation PDE and show solution works for all equations
(6,7,8)
T2-T₁
U₁(x) = ¹²=T₁ x + T₁.
L
12. u(0, t) = 100, u(1, t) = 100, f(x) = 50 x(1x), L = 1, c = 1.
An = C, and
u(x, t) = u₁(x) + u₂(x, t).
NA
|u₂(x, t) = bnet sin I,
L
(6)
(7)
(8)
n=1
u1(x)
bn = So (f(x)-(2-₁,
-x+ Ti)) sin x dx.
L
Nonzero Boundary Conditions
Consider the heat boundary value problem
8x2,
0<x<L, t> 0,
u(0, t) = T₁ and u(L, t) = T2, t>0,
u(x,0) = f(x), 0<x<L.
The problem is nonhomogeneous when T₁ and To are not both zer
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