Linear sparse differential resultant formulas

Let P be a system of n linear nonhomogeneous ordinary differential polynomials in a set U of n − 1 differential indeterminates. Differential resultant formulas are presented to eliminate the differential indeterminates in U from P. These formulas are determinants of coefficient matrices of appropriate sets of derivatives of the differential polynomials in P, or in a linear perturbation Pε of P. In particular, the formula ∂FRes(P) is the determinant of a matrix M(P) having no zero columns if the system P is “super essential”. As an application, if the system P is sparse generic, such formulas can be used to compute the differential resultant ∂Res(P) introduced by Li et al. (2011) [19].