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Algebraic Differential Equations

2017
One of the most difficult problems in the theory of Algebraic Differential Equations is to decide whether or not the solutions are meromorphic in the plane. In case this question has been answered satisfactorily, which by experience requires particular strategies adapted to the equations under consideration, there remain several major problems to be ...
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Algebraic Differential Equations

2004
Asymptotics have been much used in the study of differential equations. The method of undetermined coefficients is one common technique. At its most basic, this consists of substituting a general power series into the equation and then comparing terms in order to find the coefficients.
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Differential-Algebraic Equations

1984
In this paper we study the numerical solution of the differential/algebraic systems F(t, y, y′) = 0. Many of these systems can be solved conveniently and economically using a range of ODE methods. Others can be solved only by a small subset of ODE methods, and still others present insurmountable difficulty for all current ODE methods.
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Algebraic Schwarzian differential equations

1996
Necessary conditions for the Newton polygon associated with a general differential equation algebraic in the unknown function and its Schwarzian derivative are presented in the case of existence of an admissible solution (in Nevanlinna sense). Moreover, an admissible solution is shown to satisfy a stronger version of Nevanlinna's defect relation.
Hotzel, Richard, Jank, Gerhard
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Explicit Differential-Algebraic Equations

2020
Federico Milano   +3 more
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