HW: Solve the Partial Differential Equations by using separation of variables method: 4u xx = 0 U (0, t) = ux(1, t) = 0 u(x, 0) = f(x) = cos? nx u,(x, 0) g(r) = sin nx cos T X 0 < x < 1, t > 0, 12 0, 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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HW: Solve the Partial Differential Equations by using separation of variables method:
U1 - 4uxx = 0
Uz(0, t) = ux(1, 1) = 0
u(x, 0) = f(x) = cos? nx
u(x, 0) = g(x) = sin Tx cos TX
0 < x < 1, t > 0,
t> 0,
0<x<1,
0 <x < 1.
%3D
%3D
%3D
%3D
Answer:
t+4
u(x, t) =
cos 2nt +
sin 2nt ) cos 2n x.
Transcribed Image Text:HW: Solve the Partial Differential Equations by using separation of variables method: U1 - 4uxx = 0 Uz(0, t) = ux(1, 1) = 0 u(x, 0) = f(x) = cos? nx u(x, 0) = g(x) = sin Tx cos TX 0 < x < 1, t > 0, t> 0, 0<x<1, 0 <x < 1. %3D %3D %3D %3D Answer: t+4 u(x, t) = cos 2nt + sin 2nt ) cos 2n x.
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