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  "body": "\n## Summary\n\nThe method of steps solves a [[delay differential equation|39PCDRDB01]] with a constant delay one interval at a time.\nOn each interval of the length of the delay, the delayed term is already known, so the equation becomes an [[ordinary differential equation|0NT64JV96A]].\nIt proves existence and uniqueness of solutions forward in time, and it gives explicit solutions in simple cases.\n\n## Explanations\n\n### L1 human\n\nIf the delay is one second, then during the first second the delayed values are just the given history.\nSo one can solve an ordinary equation for the first second.\nThen this answer becomes the history for the next second, and so on.\nFor $x'(t) = -x(t - 1)$ with $x = 1$ before time $0$, the first step gives $x(t) = 1 - t$ on $[0, 1]$.\nThe second step gives $x(t) = (t - 1)(t - 3)/2$ on $[1, 2]$.\n",
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