Details:
Title  Logarithmic derivatives of solutions to linear differential equations  Author(s)  Christopher Hillar  Type  Article in Journal  Abstract  Given an ordinary differential field $K$ of characteristic zero,
it is known that if $y$ and $1/y$ satisfy linear differential
equations with coefficients in $K$, then $y'/y$ is algebraic over
$K$. We present a new short proof of this fact using Gr\"{o}bner
basis techniques and give a direct method for finding a polynomial
over $K$ that $y'/y$ satisfies. Moreover, we provide explicit
degree bounds and extend the result to fields with positive
characteristic. Finally, we give an application of our method to a
class of nonlinear differential equations.  Keywords  logarithmic derivative, linear differential equation, differential field, Gr\"{o}bner basis  Length  9 
File 
 URL 
http://arxiv.org/abs/math.AG/0309124 
Language  English  Journal  Proc. Amer. Math. Soc.  Volume  132  Number  9  Pages  26932701  Year  2004  Edition  0  Translation 
No  Refereed 
Yes  Organization 
Texas A&M University  Sponsors  Texas A&M  Conferencename  Christopher Hillar 
