HW: Solve the Partial Differential Equations by using separation of variables method: Ut - 4uxx = 0 Uz(0, t) = uz(1, t) = 0 u(x, 0) = f(x) = cos² t x u;(x, 0) = g(x)= sin² n x coS T X 0 < x < 1, t > 0, t> 0, 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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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) = uz(1, t) = 0
u(x, 0) = f(x) = cos? nx
U;(x, 0) = g(x)= sin² rx cos AX
0 < x < 1, t > 0,
t > 0,
0<x < 1,
0 <x < 1.
%3D
%3D
%3D
Answer:
t+4
u(x, t)
cos 2πt +
sin 2nt
4
cos 27 x.
Transcribed Image Text:HW: Solve the Partial Differential Equations by using separation of variables method: U1 – 4uxx = 0 Uz(0, t) = uz(1, t) = 0 u(x, 0) = f(x) = cos? nx U;(x, 0) = g(x)= sin² rx cos AX 0 < x < 1, t > 0, t > 0, 0<x < 1, 0 <x < 1. %3D %3D %3D Answer: t+4 u(x, t) cos 2πt + sin 2nt 4 cos 27 x.
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