{
  "aliases": null,
  "backlinks": [
    {
      "field": "instance_of",
      "target": "00SVP6W3CB"
    },
    {
      "field": "instance_of",
      "target": "02HB5F40VR"
    },
    {
      "field": "defines",
      "target": "0Z3YKRQZ48"
    }
  ],
  "body": "\n## Summary\n\nA linear first-order equation is an equation $y' + p(x) y = q(x)$ with given functions $p$ and $q$.\nIt is the simplest [[linear differential equation|0QQRP17Z7S]], and an [[integrating factor|07DJAZW32T]] solves it explicitly. See the [[definition|0Z3YKRQZ48]].\n",
  "commit": "545acf83a9b75c8ddc375ef8b23d2ae101a4d7e4",
  "front": {
    "kind": "concept",
    "msc": [
      "34A30"
    ],
    "name": "Linear first-order equation",
    "sources": [
      {
        "locator": "First-order equation with variable coefficients",
        "url": "https://en.wikipedia.org/wiki/Linear_differential_equation"
      }
    ],
    "tag": "07JH131FVP"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/07JH131FVP/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/07JH131FVP.md",
  "msc": [
    "34A30"
  ],
  "name": "Linear first-order equation",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/07J/07JH131FVP.md",
  "status": null,
  "tag": "07JH131FVP",
  "uri": "m2://07JH131FVP",
  "url": "https://math2.tamnd.com/wiki/linear-first-order-equation/",
  "writing": {
    "tag": "07JH131FVP",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}