Inverse Problems in Darboux Theory of Integrability
The Darboux theory of integrability for planar polynomial differential equations is a classical field, with connections to Lie symmetries, differential algebra and other areas of mathematics. In the present paper we introduce the concepts, problems and inverse problems, and we outline some recent results on inverse problems. We also prove a new result, viz. a general finiteness theorem for the case of prescribed integrating factors. Anumber of relevant examples and applications is included.
integrating factor planar polynomial vector field invariant curve elementary integrability