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Universal formulae and universal differential equations. (English) Zbl 0622.34012

By an nth order ADE \(\bar P\) is meant an algebraic differential equation of the form \(\bar P(y)=P(y,y',y'',...,y^{(n)})=0\) where P is a polynomial in \((n+1)\) variables with rational coefficients. The author proves many results including: 1) There exists a nontrivial ADE (order \(\leq 19)\), whose polynomial solutions in Q[x] are dense in C(I), for any compact interval I; 2) a theorem which is essentially a strengthened version of R. C. Buck’s result.
Reviewer: N.L.Maria

MSC:

34A99 General theory for ordinary differential equations
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