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  "body": "\n## Summary\n\nThe general solution of an [[ordinary differential equation|0P97V20RW7]] of order $n$ is a family of [[solutions|04SW7WECS8]] that depends on $n$ arbitrary constants $C_1, \\dots, C_n$.\nIn the usual case, each solution of the equation is a member of the family, with the possible exception of [[singular solutions|0Q2MDD13G4]].\nA particular solution is one solution of the equation. It is often the member of the general solution for one choice of the constants.\n\n## Remarks\n\nThe general solution of $y'' + y = 0$ is $y = C_1 \\cos x + C_2 \\sin x$. The choice $C_1 = 1$, $C_2 = 0$ gives the particular solution $y = \\cos x$.\nAn [[initial value problem|075VBY4K4X]] fixes the constants. For an equation of order $n$, one needs $n$ initial conditions.\nFor a linear equation, the [[general solution of the inhomogeneous equation|0GHWEH6H15]] is one particular solution plus the general solution of the homogeneous equation.\n\n## Explanations\n\n### L1 human\n\nThe general solution is the list of all answers, written with free constants.\nA particular solution is one answer from the list.\nFor $y' = 2x$, the general solution is $y = x^2 + C$, and $y = x^2 + 5$ is a particular solution.\n",
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