Fourth-order differential equations such as 16y'(m)y'(2) - 32y(m)y(n)y' + 17y(0(3) ) = 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 C(4).