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Solve the heat equation and find the steady state solution: uxx = ut, 0 < x...

Solve the heat equation and find the steady state solution:

uxx = ut, 0 < x < 1, t > 0, u(0,t) = T1, u(1,t) = T2, where T1 and T2 are distinct constants, and u(x,0) = 0

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