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  "body": "\n## Summary\n\nThe annihilator method finds a particular solution of a [[linear differential equation|0QQRP17Z7S]] $L y = f$ with constant coefficients.\nIt applies when the right side $f$ itself solves some homogeneous constant-coefficient equation $A f = 0$.\nApplying $A$ turns the problem into the homogeneous equation $A L y = 0$, whose solutions are known, and this tells exactly which trial functions to use.\nIt is the systematic form of the [[method of undetermined coefficients|0XRB469Z32]].\n\n## Explanations\n\n### L1 human\n\nSome right-hand sides, such as $e^{2t}$, $t^3$ or $\\cos t$, can be wiped out by a simple differential operator: $(D - 2) e^{2t} = 0$, $D^4 t^3 = 0$, $(D^2 + 1)\\cos t = 0$.\nApplying this wiping operator to both sides of the equation leaves an equation with right side zero.\nIts solutions show the exact shape of a particular solution, and only some constants remain to be found.\n",
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