Éléments de calcul infinitésimal, par m. Duhamel.

INTEGRATION DES EQUATIONS D1FFERENTIELLES. 169 ou, ce qui est plus simple, sans etre moins general, (y - ax - c) (y -t a.x -- c) -o ou (y c)2 -- a2x o= 0o Supposons plus generalement \dx] et soit a une racine quelconque de l'equation F (z) = o; on satisfera a la proposee en posant dy y - c c-Zx OI ou y- x - ou - c.OU On a done, pour une integrale quelconque, F 0)o, et, par consequent, cette derniere equation est l'integrale com.plete de la proposee. 117. Soit maintenant une equation differentielle de degre quelconque, homogene par rapport a x, y, dxO ) pdx) o) On posera - --- u; x d'ou dy x du - udx, et d4 - du - u +4- X-X dx d.x La proposee devient ainsi (+ ) +F(u ) (u \+ + ( )- o, u +a - -- F^ (a) -4- X - -+-... - (- ")0,.dx, dcl

/ 559
Pages

Actions

file_download Download Options Download this page PDF - Pages 162-181 Image - Page 162 Plain Text - Page 162

About this Item

Title
Éléments de calcul infinitésimal, par m. Duhamel.
Author
Duhamel, M. (Jean Marie Constant), 1797-1872.
Canvas
Page 162
Publication
Paris,: Gauthier-Villars,
1874-76.
Subject terms
Calculus

Technical Details

Link to this Item
https://name.umdl.umich.edu/acq9129.0002.001
Link to this scan
https://quod.lib.umich.edu/u/umhistmath/acq9129.0002.001/188

Rights and Permissions

The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain in the United States. If you have questions about the collection, please contact Historical Mathematics Digital Collection Help at [email protected]. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology at [email protected].

DPLA Rights Statement: No Copyright - United States

Manifest
https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:acq9129.0002.001

Cite this Item

Full citation
"Éléments de calcul infinitésimal, par m. Duhamel." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/acq9129.0002.001. University of Michigan Library Digital Collections. Accessed April 30, 2025.
Do you have questions about this content? Need to report a problem? Please contact us.