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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
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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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!

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
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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