A differentially algebraic replacement theorem, and analog computability
Leonard Lipshitz, Lee A. Rubel · Proceedings of the American Mathematical Society · 1987
A theorem is proved that enables one to replace a ${C^n}$ solution of a system of algebraic differential equations by analytic solutions nearby, such that each satisfies its own algebraic differential equation. As an application, we emend a proof of the Shannon-Pour-E1 thesis relating the outputs of analog computers to solutions of algebraic differential equations.