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  "body": "\n## Summary\n\nA Dirichlet boundary condition prescribes the values of the unknown function on the boundary of the domain.\nFor an ordinary differential equation on $[a, b]$, it fixes $y(a)$ and $y(b)$.\nFor a partial differential equation on a domain $\\Omega$, it fixes $u$ on the boundary $\\partial \\Omega$.\nIt is the most common type of condition in a [[boundary value problem|TM8VQJWGHZ]], next to the Neumann and Robin conditions.\nSee the [[definition|G3XFT0MWKH]].\n\n## Explanations\n\n### L1 human\n\nA Dirichlet condition says what the solution must be at the edges.\nA string with both ends nailed at height $0$ satisfies $y(a) = y(b) = 0$.\nA metal plate whose edge is held at a fixed temperature gives a Dirichlet condition for the heat equation.\nFor $y'' = 0$ on $[0, 1]$ with $y(0) = 1$ and $y(1) = 3$, the solution is the straight line $y = 1 + 2x$.\n",
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