Solution to the Heat Equation | Method of separation of variables

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This video takes you through Solution to the Heat Equation | Method of separation of variables By Mexams
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What you wrote was Ut = kUxx which transforms to become Ut - kUxx = 0. This looks like the diffusion equation

emmanuelkoranteng
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Please it looks like this is rather the diffusion equation or.... The heat equation is of the form Ut = c^2Uxx

emmanuelkoranteng