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2. Consider the 1D heat equation T(t, x) It T(t, x) dx2 x = (0, L), t> 0, (4) supplemented with the following

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2. Consider the 1D heat equation T(t, x) It T(t, x) dx2 " x = (0, L), t> 0, (4) supplemented with the following boundary conditions: T(t,0) = t,T(t, L) = 2t, for all t 0, and the initial condition (5) T(0,x) = x, x = (0, L). (6) Find a particular solution to the boundary value problem (BVP) (4)-(5); namely, complete Step 2 in the method of separation of variables.

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