An algorithm for solving second order linear homogeneous differential equations
Journal of Symbolic Computation
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
On Liouvillian solutions of homogeneous linear differential equations
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Computations with parametric equations
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Linear ordinary differential equations: breaking through the order 2 barrier
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
The general solution of an ordinary differential equation
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Parametrization of algebraic curves over optimal field extensions
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Rational parametrizations of algebraic curves using a canonical divisor
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
An algorithm for computing exponential solutions of first order linear differential systems
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Solving linear ordinary differential equations over C (x, e∫ f(x)dx)
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
About the polynomial solutions of homogeneous linear differential equations depending on parameters
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
On rational solutions of systems of linear differential equations
Journal of Symbolic Computation - Special issue on differential algebra and differential equations
An algorithm computing the regular formal solutions of a system of linear differential equations
Journal of Symbolic Computation - Special issue on differential algebra and differential equations
Liouvillian solutions of linear differential equations of order three and higher
Journal of Symbolic Computation - Special issue on differential algebra and differential equations
Rational solutions of Riccati-like partial differential equations
Journal of Symbolic Computation
On Liouvillian solutions of linear differential equations of order 4 and 5
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Tracing index of rational curve parametrizations
Computer Aided Geometric Design
Solutions of linear ordinary differential equations in terms of special functions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Implicitization of differential rational parametric equations
Journal of Symbolic Computation
Algebraic general solutions of algebraic ordinary differential equations
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Rational solutions of ordinary difference equations
Journal of Symbolic Computation
Rational general solutions of first order non-autonomous parametrizable ODEs
Journal of Symbolic Computation
Polynomial general solutions for first order autonomous ODEs
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
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We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For an autonomous first order ODE, we give an algorithm to compute a rational general solution if it exists. The algorithm is based on the relation between rational solutions of the first order ODE and rational parametrizations of the plane algebraic curve defined by the first order ODE and Padé approximants.