## 423 Citations

Algorithms for Solving Linear Ordinary Differential Equations

- Mathematics, Computer Science
- 1998

The new domain of linear ordinary differential operators is presented and how it works in a few examples and in a very informal way the algebraic point of view dealing with ordinary differential equations is introduced.

A Polynomial Algorithm for Finding Rational General Solutions of First Order Autonomous Ordinary Differential Equations

- Mathematics
- 2016

: In this paper we give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For first order autono9mous ODE F=0, we give an exact degree bound for its…

Algorithms for Solving Linear Differential Equations with Rational Function Coefficients

- Mathematics
- 2017

This thesis introduces two new algorithms to find hypergeometric solutions of second order regular singular differential operators with rational function or polynomial coefficients. Algorithm 3.2.1…

Rational general solutions of algebraic ordinary differential equations

- MathematicsISSAC '04
- 2004

An algorithm to compute a rational general solution if it exists is given based on the relation between rational solutions of the first order ODE and rational parametrizations of the plane algebraic curve defined by thefirst order ODR and Padé approximants.

An algorithm for computing a standard form for second-order linear q-difference equations

- Mathematics
- 1997

Algebraic general solutions of algebraic ordinary differential equations

- Mathematics, Computer ScienceISSAC
- 2005

For a first order autonomous ODE, the optimal bound for the degree of its algebraic general solutions is given and a polynomial-time algorithm to compute an algebraicgeneral solution if it exists is given.

How to solve linear differential equations: An outline

- MathematicsProgramming and Computer Software
- 2007

This paper gives an overview of how the differential Galois theory leads to algorithms to find the Liouvillian solutions, and outlines the general ideas and results.

Solving Orthogonal Matrix Differential Systems in Mathematica

- MathematicsInternational Conference on Computational Science
- 2002

A component of a new environment for the numerical solution of ordinary differential equations in Mathematica is outlined. We briefly describe how special purpose integration methods can be…

Integration and Differential Equations in Computer Algebra

- Mathematics, Computer Science
- 1992

We describe in this paper how the problems of computing indeenite integrals and solving linear ordinary diierential equations in closed form are now solved by computer algebra systems. After a brief…

An algebraic method for quasi-linear first-order ODEs

- Mathematics
- 2018

In this paper, we consider the class of quasi-linear first-order ODEs of the form y ′ = P(x; y), where P is a polynomial in y with coefficients in ℂ(x ), and study their algebraic solutions. Our…

## References

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An implementation of Kovacic's algorithm for solving second order linear homogeneous differential equations

- MathematicsSYMSAC '81
- 1981

A version of Kovacic's algorithm for the closed form solution of differential equations of the form ay" + by' + cy &equil; 0, where a, b, and c are rational functions with complex coefficients of the independent variable x is described.

Solving homogeneous linear differential equations in terms of second order linear differential equations

- Mathematics
- 1985

Soit F un corps differentiel de caracteristique zero et soit L(y)=0 une equation differentielle lineaire homogene d'ordre n a coefficients dans F. On developpe des conditions necessaires et…

Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations

- Mathematics
- 1981

be a linear differential operator with coefficients in F, a finite algebraic extension of Q(x). We shall show that one can find, in a finite number of steps, a basis for the vector space of…

A discussion and implementation of Kovacie's algorithm for ordinary differential equations

- University of Waterloo Computer Science Department Research Report CS-84-35
- 1984

An introduction to differential algebra, Actualités Sci

- Ind., No. 1251 = Publ. Inst. Math. Univ. Nancago,
- 1957

A tLrtorial introduction to MAPLE

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- 1986

An algorithm for solving second order linear homogeneous differential equations

- J. Symbolic Comput
- 1986