All LCCODEs (linear, constant-coefficient ordinary differential equation) with initial rest conditions describe causal LTI systems (is this a correct statement?)
- Is the converse true, i.e. can all causal LTI systems be described by LCCODEs with initial rest? If not, what are the necessary/sufficient conditions?
It seems trivial that arbitrary differential/difference equations describe some sort of system (is that also true?)
- Again, is the converse true, i.e. can we describe any arbitrary systems with (possibly nonlinear/variable-coefficient/partial, without restriction on initial conditions) differential equations? If not, what are the necessary/sufficient conditions?