Geodesic
On first integrals for polynomial differential equations on the line
Studia Mathematica, Tome 107 (1993) no. 2, pp. 205-211

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that any equation dy/dx = P(x,y) with P a polynomial has a global (on ℝ²) smooth first integral nonconstant on any open domain. We also present an example of an equation without an analytic primitive first integral. 
Henryk Żołądek. On first integrals for polynomial differential equations on the line. Studia Mathematica, Tome 107 (1993) no. 2, pp. 205-211. doi: 10.4064/sm-107-2-205-211
@article{10_4064_sm_107_2_205_211,
     author = {Henryk \.Zo{\l}\k{a}dek},
     title = {On first integrals for polynomial differential equations on the line},
     journal = {Studia Mathematica},
     pages = {205--211},
     year = {1993},
     volume = {107},
     number = {2},
     doi = {10.4064/sm-107-2-205-211},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-107-2-205-211/}
}
TY  - JOUR
AU  - Henryk Żołądek
TI  - On first integrals for polynomial differential equations on the line
JO  - Studia Mathematica
PY  - 1993
SP  - 205
EP  - 211
VL  - 107
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-107-2-205-211/
DO  - 10.4064/sm-107-2-205-211
LA  - en
ID  - 10_4064_sm_107_2_205_211
ER  - 
%0 Journal Article
%A Henryk Żołądek
%T On first integrals for polynomial differential equations on the line
%J Studia Mathematica
%D 1993
%P 205-211
%V 107
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-107-2-205-211/
%R 10.4064/sm-107-2-205-211
%G en
%F 10_4064_sm_107_2_205_211

Cité par Sources :