I have a function $f(x)$ defined in $\Bbb R$ with $f$ smooth and I would to find the linear differential equation with constant coefficients that generates it (or at least the best fit of it).
The order of the equation can be $n$ as high as you want but $n$ is finite. The LCCODE Is surely not a base of $\Bbb C$ infinity if $n$ is finite.
I am thinking more of a numerical approach maybe with machine learning. It is like a fit but for functions.