A differentially algebraic elimination theorem with application to analog computability in the calculus of variations
Lee A. Rubel, Michael F. Singer · Proceedings of the American Mathematical Society · 1985
An elimination theorem is proved in differential algebra, from which it follows that an analytic solution of virtually any ordinary differential equation that you can "write down" must actually solve an algebraic differential equation. As a corollary, it follows that the solutions of a large class of variational problems can be produced by an analog computer.