E95 -- De aequationibus differentialibus, quae certis tantum casibus integrationem admittunt

(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.

According to the records, it was presented to the St. Petersburg Academy on February 17, 1738.

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