Geodesic
The transvectants and the integrals for Darboux systems of differential equations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 4-18

Voir la notice de l'article provenant de la source Math-Net.Ru

We apply the algebraic theory of invariants of differential equations to integrate the polynomial differential systems $dx/dt=P1_(x,y)+xC(x,y)$, $dy/dt=Q1_(x,y)+yC(x,y)$, where real homogeneous polynomials $P_1$ and $Q_1$ have the first degree and $C(x,y)$ is a real homogeneous polynomial of degree $r\ge 1$. In generic cases the invariant algebraic curves and the first integrals for these systems are constructed. The constructed invariant algebraic curves are expressed by comitants and invariants of investigated systems. 
@article{BASM_2008_1_a1,
     author = {V. Baltag and I. Calin},
     title = {The transvectants and the integrals for {Darboux} systems of differential equations},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {4--18},
     publisher = {mathdoc},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2008_1_a1/}
}
TY  - JOUR
AU  - V. Baltag
AU  - I. Calin
TI  - The transvectants and the integrals for Darboux systems of differential equations
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2008
SP  - 4
EP  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2008_1_a1/
LA  - en
ID  - BASM_2008_1_a1
ER  - 
%0 Journal Article
%A V. Baltag
%A I. Calin
%T The transvectants and the integrals for Darboux systems of differential equations
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2008
%P 4-18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2008_1_a1/
%G en
%F BASM_2008_1_a1
V. Baltag; I. Calin. The transvectants and the integrals for Darboux systems of differential equations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 4-18. http://geodesic.mathdoc.fr/item/BASM_2008_1_a1/