Equivalence problem and integrability of the Riccati equations (Q976942)

By considering the Lie group and Lie algebra of equivalence transformations, the authors derive some criteria for the equivalence and integrability of general real Riccati equations. The criteria are based on locally defined invariants and differential invariants of equivalence transformations. This approach avoids complicated calculations as only a few simple expressions are compared to find out whether two Riccati equations are equivalent.