Since distributions can not be multiplied ,then does the following equation (ODE)
$$ xy'(x)= \delta (x) $$
has a solution? Here $\delta$ is the Dirac delta function.
2026-04-04 21:15:18.1775337318
Differential equation and distribution theory
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The solutions to this ODE are $$ y(x) = -\delta(x) + aH(x) + b, $$ where $a,b$ are constants and $H$ is the Heaviside step function.