Fontaine’s forgotten method for inexact differential equations. (English) Zbl 1398.34006
Summary: In 1739 Alexis-Claude Clairaut published the modern integrating factor method of solving inexact ordinary differential equations (ODEs). He was motivated by a 1738 Alexis Fontaine paper with a different method which requires solving a difficult partial differential equation (PDE). Here we revisit Fontaine’s method, examine his modest attempt to solve the PDE, and utilize a different technique to give (we believe) the first family of ODEs solvable by Fontaine’s method with no obvious solution using the modern technique.
MSC:
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
References:
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