A day in the life of a phaggot ^w^

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This time, I'm trying to discover the heat equation, so far the curve that best fits is something around and , so I was wondering if you could give me any hints into it. I understand that this is just the expressed form of the actual equation that might involve differential equations (though I don't know much about that kind of maths but still then I have been able to express the equation of the spring or the pendulum using differential equations even though I didn't know how to solve them) but I imagine that it might be related to expressing the difference between a and when they are close enough. And as I'm saying I'm mostly looking for some guidance into this, and to know if I'm following a good approach, and perhaps any ideas as to how I can verify if to curves are sufficiently similar given some table of data.