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8. (6 points) Solve the heat equation tu=kx22u,0 0 subject to the boundary conditions xu(0,t)=0xu(L,t)=0t>0t>0 and the initial condition u(x,0)=5cosL2x Determine for your solution if

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8. (6 points) Solve the heat equation tu=kx22u,00 subject to the boundary conditions xu(0,t)=0xu(L,t)=0t>0t>0 and the initial condition u(x,0)=5cosL2x Determine for your solution if it is the unique solution of this

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