#### English Title

Example of the construction of equations

#### Enestrom Number

28

#### Fuss Index

250

#### Original Language

Latin

#### English Summaries

In this paper, Euler investigates a differential equation that he encountered in finding the arc length of an ellipse. This differential equation cannot be solved by separation of variables, as is indicated in the title of the article. Euler first develops a formula for the arc length of an ellipse by cleverly manipulating a binomial series, then shows that this formula satisfies the desired differential equation. Integrating factors make a brief appearance.

#### Published as

Journal article

#### Published Date

1738

#### Written Date

1733

#### Content Summary

In this paper, Euler investigates a differential equation that he encountered in finding the arc length of an ellipse. This differential equation cannot be solved by separation of variables, as is indicated in the title of the article. Euler first develops a formula for the arc length of an ellipse by cleverly manipulating a binomial series, then shows that this formula satisfies the desired differential equation. Integrating factors make a brief appearance.

#### Original Source Citation

Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 168-174.

#### Opera Omnia Citation

Series 1, Volume 20, pp.1-7.

#### Record Created

2018-09-25