In this paper we study non-autonomous algebraic ODEs F(x, y, y) = 0, where F(x, y, z) ∈ Q[x, y, z], provided a proper rational parametrization P (s, t) of the corresponding algebraic surface F(x, y,… (More)

We describe a group of birational transformations acting on the set of algebraic ordinary differential equations (AODEs) of arbitrary order n. This transformation group, by its action, partitions the… (More)

In this paper, we introduce a group of affine linear transformations and consider its action on the set of parametrizable algebraic ODEs. In this way the set of parametrizable ODEs is partitioned… (More)

In this paper, we provide an algorithm to compute explicit rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its rational invariant algebraic curves.… (More)

We consider the following main problem: “Given a trivariate polynomial F (x, y, z), decide the existence of a rational general solution of the algebraic ODE F (x, y, y′) = 0 of order 1; in the… (More)

Parametric variation control was simulated using key FDC sensors identified through multivariate modeling of Back End Of Line (BEOL) process equipment in a 65nm mass production line. The simulation… (More)

In this paper we provide an algorithm to find explicitly rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its invariant algebraic curves. The method… (More)

In this paper, we generalize the results of Ngô and Winkler [18, 20, 21] to the case of high order non-autonomous algebraic ODE with a birational parametrization of the corresponding algebraic… (More)

a r t i c l e i n f o a b s t r a c t The notion of strict equivalence for order one differential equations of the form f (y , y, z) = 0 with coefficients in a finite extension K of C(z) is… (More)