Your time ODE should be equivalent to T = cT. For convenience, choose the separation constant...

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Your time ODE should be equivalent to T = cT. For convenience, choose the separation constant c to be -ak for some real number k. Solve this time equation to get one linearly independent function of time. We physically want the temperature to reach a steady state rather than blow up to infinity. Why does this imply that the separation constant c, should be negative, as we used? Your time ODE should be equivalent to T = cT. For convenience, choose the separation constant c to be -ak for some real number k. Solve this time equation to get one linearly independent function of time. We physically want the temperature to reach a steady state rather than blow up to infinity. Why does this imply that the separation constant c, should be negative, as we used?

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