E95 -- De aequationibus differentialibus, quae certis tantum casibus integrationem admittunt
(On differential equations which admit integration only in certain cases)
Summary:
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.
Publication:
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Originally published in Commentarii academiae scientiarum Petropolitanae 10, 1747, pp. 40-55
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Opera Omnia: Series 1, Volume 22, pp. 162 - 180
Documents Available:
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