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  "body": "\n## Summary\n\nIn a delay differential equation, the rate of change at time $t$ depends on the state at earlier times, such as $t - \\tau$.\nTo solve it, one must give the whole history of the solution on an initial interval, not just one initial value.\nSo the natural state space is a space of functions, and the equation is infinite-dimensional even for one unknown.\nDelay equations model systems with reaction times, such as feedback control, population dynamics and epidemics.\n\n## Explanations\n\n### L1 human\n\nA shower whose temperature responds to the tap only after a few seconds is a classic picture of delay.\nYou react to the water you feel now, which reflects the tap setting of a moment ago, and so you tend to overshoot.\nThe equation $x'(t) = -x(t - 1)$ says that the state decreases at a rate given by its value one time unit earlier.\nUnlike $x' = -x$, which only decays, this equation has oscillating solutions.\n",
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