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  "body": "\n## Summary\n\nThe Sumudu transform of a function $f$ on $[0, \\infty)$ is $G(u) = \\int_0^\\infty f(ut)\\, e^{-t}\\, dt$.\nIt is the [[Laplace transform|0V49JEZW06]] in disguise: $G(u) = \\frac{1}{u} F\\big(\\frac{1}{u}\\big)$, where $F$ is the Laplace transform of $f$.\nIts appeal is that it keeps units and scales: it sends $t^n$ to $n!\\, u^n$ and constants to the same constants.\nIt is used, like the Laplace transform, to solve linear differential equations with constant coefficients.\n\n## Explanations\n\n### L1 human\n\nThe transform averages $f$ along the stretched line $t \\mapsto f(ut)$, with exponentially decaying weights.\nBecause the weights $e^{-t}$ have total mass $1$, a constant function is sent to itself.\nA power $t^n$ is sent to $n!\\, u^n$, so a polynomial becomes a polynomial in $u$ of the same degree.\nThe variable $u$ plays the role of a time scale.\n",
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