Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia Robinson had negatively settled Hilbert 10th problem, I wonder if there is an analog result to the differential equations ?
2026-04-01 01:02:37.1775005357
Is there a way to decide whether a differential equation is solvable or not?
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There is newer stuff, but you can find a partial answer in an old short paper Some Recursively Unsolvable Problems in Analysis (Adler, AMS Proceedings, 1969). It is shown that there is no algorithm for determining the solvability of systems of algebraic differential equations. This is done by a reduction to the result by Davis, Putnam, Robinson on the nonexistence of an algorithm for determining whether an exponential Diophantine equation has a solution.