Differential elimination with Dixon resultants

In this paper we apply the idea of Dixon resultant to algebraic differential equations and introduce the Dixon differential resultant. We prove that a necessary condition for the existence of a common solution of two algebraic differential equations is that the differential resultant is equal to zero, which actually provides a method of elimination and reduces a system of multi-variate differential equations to a system of single-variate differential equations. This result is also generalized to the system of n differential polynomials. We give algorithms to realize our method of elimination for systems of differential equations. Our results and algorithms are demonstrated by some examples.