That arbitrary computation could be described with differential equations is an immediate corollary of Turing's 1936 paper: because a Turing machine could be co

That arbitrary computation could be described with differential equations is an immediate corollary of Turing's 1936 paper: because a Turing machine could be constructed in the physical world, its operation can be described with differential equations. An immediate corollary of that is that differential equations are undecidable (i.e. differentiability does not give us more power). For a specific represnetation of TMs with ODEs see: https://link.springer.com/chapter/10.1007%2F11494645_21 https://link.springer.com/chapter/10.1007%2F11494645_21