b) Consider the heat equation ди 2²u Ət with boundary conditions = and initial conditions ur(0, t) = 0, u. (1, t) = 0, t> 0, 0 0, u(x, 0) { 0, 2.x, 0

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b) Consider the heat equation
ди 2²u
Ət
with boundary conditions
=
and initial conditions
ur(0, t) = 0, u,(1, t) = 0, t> 0,
0<x< 1, t> 0,
u(x, 0) {
0,
2.x,
0<x<0.5.
0.5 < x < 1.
Use the method of separation of variables to solve the equation.
Transcribed Image Text:b) Consider the heat equation ди 2²u Ət with boundary conditions = and initial conditions ur(0, t) = 0, u,(1, t) = 0, t> 0, 0<x< 1, t> 0, u(x, 0) { 0, 2.x, 0<x<0.5. 0.5 < x < 1. Use the method of separation of variables to solve the equation.
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