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Fourth-order differential equations such as 16y′my′2 - 32ymyny′ + 17y03 = 0 are developed. It is shown that the equation is “universal” in the sense that any continuous function can be approximated with arbitrary accuracy over the whole x axis by a solution y(x) of the equation. This solution is a piecewise polynomial of degree 9 and of class C4.
Keywords: approximation theory, polynomial splines
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