On the Equivalence Problem of Generalized Abel ODEs under the Action of   the Linear Transformations Pseudogroup
  In the present paper we establish the necessary and sufficient conditions for two generalized Abel differential equations to be locally equivalent under the action of the pseudogroup of linear transformations of the form $\{x\mapsto f(x),~ y\mapsto g(x)\cdot y + h(x)\}$. These conditions are formulated in terms of differential invariants. 
Vadim V. Shurygin Jr
math.DG math.CA