The aim of this paper is to construct the analytic vector fields with given as trajectories or solutions. In particular we construct the polynomial vector field from given conics (ellipses, hyperbola, parabola, straight lines) and determine the differential equations from a finite number of solutions.
@article{urn:eudml:doc:40250,
title = {Differential equations on the plane with given solutions.},
journal = {Collectanea Mathematica},
volume = {47},
year = {1996},
pages = {145-177},
zbl = {0855.34017},
mrnumber = {MR1402067},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40250}
}
Ramírez, R.; Sadovskaia, N. Differential equations on the plane with given solutions.. Collectanea Mathematica, Tome 47 (1996) pp. 145-177. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40250/