|
|||||
|
|
|
|
|
|
|
|
|
Algebraic
independence of solutions of differential equations of the
second order
Michel Brestovski |
|
Vol. 140 (1989), No. 1, 1–19
|
Abstract |
|
We deal with second order algebraic differential equations obtained by equating exact and logarithmic derivatives. Under the assumption that such an equation has no “first integral” (which is proven in particular cases), it is shown that two generic solutions can be algebraically independent only if they satisfy a “very special” relation. Whence is deduced the existence of an infinite algebraically free set of generic solutions over a constant differential field. |
Mathematical Subject Classification 2000
Primary: 12H05
Secondary: 12H20
|
Milestones
Received: 20 July 1983
Revised: 30 January 1989
Published: 1 November 1989
|
Authors |
| Michel Brestovski | |
|
