This paper presents an algorithm to compute invariants of the differential Galois group of linear differential equations L(y) = 0: if V(L) is the vector space of solutions of L(y) = 0, we show how… Expand

We compute the liouvillian solutions rn.--1 of L ( y ) = y" r y = 0 by computing the minimal polynomial P ( u ) = u '~ + ~i=0 bi ul of an algebraic solution of R i ( u) = u ~ ao a l u + u s = O.Expand

We present algorithms for computing rational and hyperexponential solutions of linear D-finite partial differential systems written as integrable connections by adapting existing algorithms handling ordinary linear differential systems.Expand

We show how, by carefully combining the techniques of those algorithms, one can find the Liouvillian solutions of an irreducible second order linear differential equation by computing only rational solutions of some associated linear differential equations.Expand

We investigate a generalization of the three-dimensional spring-pendulum system. The problem depends on two real parameters (k, a), where k is the Young modulus of the spring and a describes the… Expand

We present alternative algorithms for computing symmetric powers of linear ordinary differential operators with coefficients in arbitrary integral domains and become faster than the traditional methods.Expand

We give an algorithm for solving second order differential by pullbacks for a general differential field k by constructing new formulas which rely on invariants only.Expand

(2) Lry ≡ ∂y − r(x)y = 0 where r(x) = A1 4 + A1 2 −A2 Given two linearly independent solutions of (1), say y1, y2, either formal or actual, the differential fieldK generated byK, y1 and y2 is called… Expand