On differential equations which admit integration only in certain cases
Euler starts with a second-order linear differential equation with simple, rational coefficients and figures out which cases of this quantity, divided by infinite sequences, produce a quotient that can be integrated. Then he derives a first-order differential equation out of the given equation and gets a new integrable equation in this way. The Riccati differential equation appears as a special case.
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 10, pp. 40-55.
Opera Omnia Citation
Series 1, Volume 22, pp.162-180.