On the Equivalence Problem of Generalized Abel ODEs under the Action of the Linear Transformations Pseudogroup

摘要

In the present paper we establish the necessary and sufficient conditions fortwo generalized Abel differential equations to be locally equivalent under theaction of the pseudogroup of linear transformations of the form $\{x\mapstof(x),~ y\mapsto g(x)\cdot y + h(x)\}$. These conditions are formulated in termsof differential invariants.