Copyright © 2018 Rocky Mountain Mathematics Consortium. We improve the known expressions of the Cr differential systems in the plane having a given Cr+1 invariant curve, or a given Cr+1 first integral. Their application to polynomial differential systems having either an invariant algebraic curve, or a first integral, also improves the known results on such systems.
- Cr function
- Darboux theory of integrability
- Exponential factor
- Invariant curve
- Planar differential system