Galois Groups of Second and Third Order Linear Differential Equations

Galois Groups of Second and Third Order Linear Differential Equations

Using the representation theory of groups, we are able to give simple necessary and suucient conditions regarding the structure of the galois groups of second and third order linear diierential equations. These allow us to give simple necessary and suucient conditions for a second order linear diierential equation to have liouvillian solutions and for a third order linear diierential equation t...

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Computing the differential Galois group of a one-parameter family of second order linear differential equations

We develop algorithms to compute the differential Galois group corresponding to a one-parameter family of second order homogeneous ordinary linear differential equations with rational function coefficients. More precisely, we consider equations of the form ∂2Y ∂x2 + r1 ∂Y ∂x + r2Y = 0, where r1,r2 ∈C(x, t) and C is an algebraically closed field of characteristic zero. We work in the setting of ...

Lie symmetries and differential Galois groups of linear equations

For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In connection with this a new algorithm for computing the Lie symmetries of a linear ordinary differen...

Second Order Linear and Nonlinear Differential Equations'