Loading...
Please wait, while we are loading the content...
Similar Documents
On Liouvillian Solutions of Third Order Homogeneous Linear Differential Equations
| Content Provider | Scilit |
|---|---|
| Author | Okko, Noura |
| Copyright Year | 2019 |
| Description | In this article we will consider third order homogeneous differential equations: L(y)=y'''+a_1y'+a_0y(a_0,a_1 ∈k) whose Galois group G（L） is imprimitive. This case is characterised by the fact that the third symmetric power equation L ^ⓢ3(y)=0 has an exponential solution whose square is rational (Singer & Ulmer 1993). If L(y)=0 has a Liouvillian solution z whose logarithmic derivative u=z'/z is algebraic over a differential field (k,') ,we will give an algorithm to find the relation between a_0, a_1 , the semi-invariant S=Y_1Y_2Y_3 which is unique up to multiplication by a constant, the coefficients C_0, C_1 of the minimal polynomial P(u) of u and their derivatives. The aim of this work is to diminutize the number of constants C_m stated in the algorithm of Singer & Ulmer (Singer & Ulmer 1993 Algorithm p. 31) whose determination is not easy to do, and we will achieve this by using Groebner Basis. |
| ISSN | 19169795 |
| e-ISSN | 19169809 |
| DOI | 10.5539/jmr.v11n3p14 |
| Journal | Journal of Mathematics Research |
| Issue Number | 3 |
| Volume Number | 11 |
| Language | English |
| Publisher | Canadian Center of Science and Education |
| Publisher Date | 2019-05-08 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Physics Diï |
| Content Type | Text |
| Resource Type | Article |
