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  "body": "\n## Summary\n\nA differential-algebraic system of equations, or DAE, is a system $F(t, x, x') = 0$ that cannot be solved for the derivative $x'$.\nTypically some equations contain derivatives and others are pure constraints between the unknowns.\nSuch systems arise in electrical circuits, in constrained mechanics and in chemical engineering.\nSee the [[definition|FD7H5AM1R7]].\n\n## Explanations\n\n### L1 human\n\nAn ordinary differential equation tells how every unknown changes in time.\nIn a DAE some unknowns have no equation for their rate of change; they are tied to the others by algebraic rules instead.\nA pendulum written in Cartesian coordinates is an example: the position moves by Newton's law, but it must also stay at a fixed distance from the pivot.\nBecause of the constraints, the starting values cannot be chosen freely.\n",
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