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  "body": "\n## Definition\n\nLet $F\\left(x, y, y', \\dots, y^{(n)}\\right) = 0$ be an [[ordinary differential equation|0P97V20RW7]] for an unknown function $y$ of $x$.\nIts order is the largest integer $k$ such that the equation depends on the derivative $y^{(k)}$.\nFor a system of equations, the order is the largest order of a derivative that occurs in the system.\n\n## Remarks\n\nThe equation $y' = x y$ has order $1$, and the equation $y'' + \\sin y = 0$ has order $2$.\nThe order does not depend on the powers of the derivatives: $(y')^3 = y$ has order $1$.\nAn equation of order $n$ can be changed into a first-order system of $n$ equations. See [[reduction to a first-order system|0TH9CPW3VS]].\n\n## Explanations\n\n### L1 human\n\nThe order tells you how many times the unknown function is differentiated, at most.\nAn equation with $y'$ only is of first order. An equation with $y''$, but no higher derivative, is of second order.\n",
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