E251 -- De integratione aequationis differentialis \(\frac{m dx}{\sqrt{}(1-x^4)} = \frac{n dy}{\sqrt{}(1-y^4)} \)

(On the integration of the differential equation \(\frac{m dx}{\sqrt{}(1-x^4)} = \frac{n dy}{\sqrt{}(1-y^4)} \))


Euler takes it for granted that \(\frac{m}{n}\) is a rational number. In addition to the equation given in the title, Euler also handles the cases where there is an arbitrary whole fourth-degree function or a special 6th-degree function under the radical sign.

According to the records, it was presented to the St. Petersburg Academy on April 30, 1753.

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