In this paper, we study unirational differential curves and the corresponding differential rational parametrizations. We first investigate basic properties of proper differential rational parametrizations for unirational differential curves. Then we show that the implicitization problem of proper linear differential rational parametric equations can be solved by means of differential resultants. Furthermore, for linear differential curves, we give an algorithm to determine whether an implicitly given linear differential curve is unirational, and in the affirmative case, to compute a proper differential rational parametrization for the differential curve.

中文翻译：

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单调微分曲线和微分有理参数

在本文中，我们研究了单边微分曲线和相应的微分有理参数。我们首先研究非微分微分曲线的适当微分有理参数化的基本性质。然后，我们证明了适当的线性微分有理参数方程的隐式问题可以通过微分结果来解决。此外，对于线性微分曲线，我们给出一种算法来确定隐式给定的线性微分曲线是否不成比例，并且在肯定的情况下，为该微分曲线计算适当的微分有理参数。