Linear sparse differential resultant formulas

Let $\text{cP}$ 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 $\text{cP}$. These formulas are determinants of coefficient matrices of appropriate sets of derivatives of the differential polynomials in $\text{cP}$, or in a linear perturbation ${\text{cP}}_{\epsilon }$ of $\text{cP}$. In particular, the formula $\text{dfres}(\text{cP})$ is the determinant of a matrix $\text{cM}(\text{cP})$ having no zero columns if the system $\text{cP}$ is “super essential”. As an application, if the system $\mathfrak{P}$ is sparse generic, such formulas can be used to compute the differential resultant $\text{dres}(\mathfrak{P})$ introduced by Li, Gao and Yuan in (Proceedings of the ISSAC’2011).