If well any smooth curve can be represented as the solution of a differential equations, what happen if we want solutions that are forced to satisfy certain constraint? Can we derived a stricter smaller family of differential equations that serve as universal approximations of curves satisfying such constrain? This is definitely what we do with algebraic differential equations, but it will be interesting to see how this can be simplified.
If well any smooth curve can be represented as the solution of a differential equations, what happen if we want solutions that are forced to satisfy certain constraint? Can we derived a stricter smaller family of differential equations that serve as universal approximations of curves satisfying such constrain? This is definitely what we do with algebraic differential equations, but it will be interesting to see how this can be simplified.