Differential Nullstellensatz is a fundamental theorem in the algebraic theory of differential equations. It states that, if a system of algebraic differential equations does not have a solution in any extension of the coefficient field, then 1 can be expressed as a polynomial linear combination of the derivatives of the equations of the original system up to some order. Thus, finding bounds for this order is a key ingredient of algorithmic treatment of solvability of differential equations and related questions. We will present a new and improved bound for the effective version of the differential Nulstellensatz and discuss some differential-algebraic problems arising in the proof. This is joint work with Alexey Ovchinnikov and Thieu Vo Ngoc.
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