On arithmetic properties of the solutions of a universal differential equation at algebraic points (Q5937664)

The object of the paper is to investigate the \(C^\infty\)-solutions at algebraic points to an universal fifth-order algebraic differential equation (ADE) of the form NEWLINE\[NEWLINEP(y',y'',\dots, y^{(5)})= 0.\tag{1}NEWLINE\]NEWLINE It is shown that there is a nontrivial ADE of the form (1) such that any real continuous function on the whole real line can be uniformly approximated by a sequence \((y_n)_{n\geq 1}\) of \(C^\infty(\mathbb R)\)-solutions to this ADE.