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  "body": "\n## Summary\n\nA differential inclusion is a relation $x'(t) \\in F(t, x(t))$, where $F$ is a [[multivalued function|03CPD1HGF3]] that gives a set of allowed velocities at each time and state.\nIt generalizes the [[ordinary differential equation|0NT64JV96A]] $x' = f(t, x)$, which is the case where each set $F(t, x)$ has one element.\nDifferential inclusions describe control systems, equations with discontinuous right side, and systems with uncertain data.\n\n## Explanations\n\n### L1 human\n\nAn ordinary differential equation prescribes one velocity at each point.\nA differential inclusion only prescribes a set of possible velocities, and a solution may choose any of them at each moment.\nSo there are usually many solutions from one starting point, like the many paths of a driver who may choose any speed below a limit.\nFor example, the solutions of $x'(t) \\in [-1, 1]$ are the functions whose slope never exceeds $1$ in absolute value, such as $x(t) = \\sin t$ or $x(t) = \\abs{t}$.\n",
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