The First Integrals of a Second Order Ordinary Differential Equation and Application

A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION

Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...

An efficient numerical method for singularly perturbed second order ordinary differential equation

In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...

Ju l 2 00 5 Finding Elementary First Integrals for Rational Second Order Ordinary Differential Equations

Here we present an algorithm to find elementary first integrals of rational second order ordinary differential equations (SOODEs). In [17], we have presented the first algorithmic way to deal with SOODEs, introducing the basis for the present work. In [18], the authors used these results and developed a method to deal with SOODEs and a classification of those. Our present algorithm is based on ...

Liouvillian First Integrals of Second Order Polynomial Differential Equations

We consider polynomial differential systems in the plane with Liouvillian first integrals. It is shown that all such systems have Darbouxian integrating factors, and that the search for such integrals can be reduced to a search for the invariant algebraic curves of the system and their ‘degenerate’ counterparts.

A method for solving first order fuzzy differential equation