  We use the solution space of a pair of ODEs of at least second order to
construct a smooth surface in Euclidean space. We describe when this surface is
a proper embedding which is geodesically complete with finite total Gauss
curvature. If the associated roots of the ODEs are real and distinct, we give a
universal upper bound for the total Gauss curvature of the surface which
depends only on the orders of the ODEs and we show that the total Gauss
curvature of the surface vanishes if the ODEs are second order. We examine when
the surfaces are asymptotically minimal.
