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2. Consider the heat equation with homogenous boundary conditions: 1-2 at d , 0<x<12,t > 0 u(0,t)- u(2,t)-0 Verify that u.-e, sin(2x) and«,ะเ 2, sin(2x) are solutions to the above (a) equation. (5 marks) (b) Use the principle of superposition and the functions u‘ and u, to construct u( ) that satisfies the initial condition: u(x,0)-12 sin7sin(2x) (4 marks)
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