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  "body": "\n## Definition\n\nLet $n \\ge 1$ be an integer, let $U$ be a subset of $\\mathbb{R}^{n+2}$, and let $F : U \\to \\mathbb{R}$ be a function.\nAn ordinary differential equation of [[order|0XK0G19SK8]] $n$ is an equation\n$$F\\left(x, y, y', \\dots, y^{(n)}\\right) = 0$$\nfor an unknown real function $y$ of one real variable $x$. Here $y^{(k)}$ is the $k$-th derivative of $y$.\nThe equation must depend on $y^{(n)}$.\nIf $y$ takes values in $\\mathbb{R}^m$ and $F$ takes values in $\\mathbb{R}^m$, the equation is a system of $m$ ordinary differential equations.\n\n## Remarks\n\nThe word ordinary means that the unknown function depends on one variable only. An equation with partial derivatives of a function of several variables is a partial differential equation.\nThe equation is in [[explicit form|08WWTN738R]] when it is solved for the highest derivative: $y^{(n)} = f\\left(x, y, y', \\dots, y^{(n-1)}\\right)$.\nA [[solution|07VX34QXAV]] is a function on an interval that satisfies the equation at each point of the interval.\n\n## Explanations\n\n### L1 human\n\nAn ordinary differential equation is a rule that links a function of one variable with its derivatives.\nFor example, $y'' + y = 0$ links $y$ with its second derivative. The functions $\\sin x$ and $\\cos x$ satisfy it.\n",
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