Éléments de calcul infinitésimal, par m. Duhamel.

I96 LIVRE IV. Soit, en effet, z =f(x, a) cette valeur de z. Posons rx rx y= f (fx, a) dc a z dc; nous en deduirons dy _, rxdf (x, a) f =/(X, Xf d)a. dxy o dx Mais, par hypothese, f(a, a) est nul, quel que soit a done f (x, x) = o, et l'on a seulement dr r dz. On trouvera de mmem d2r rX d2z dx ----2 d;,.... dm - _ xdI dz dm-V')" df'ry f'd'.Z dxE'- F dxJ da. Substituant ay et a ses derivees les valeurs ainsi obtenues dans 1'equation (i), elle devient rx dmz dm-'z +A- - -... Uz) d + F F(x), k dx'" dx"ro- d n ce qui est une identite en vertu de l'6quation (2). Connaissant ainsi une solution de l'equation (i), on aura son integrale generale, en y ajoutant l'integrale generale de l'equation (2). Cas particulier olt le premier memnbre n a qu'un seal terme. 1 35. Si, dans l'equation (i), tous les coefficients sont nuls,

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Title
Éléments de calcul infinitésimal, par m. Duhamel.
Author
Duhamel, M. (Jean Marie Constant), 1797-1872.
Canvas
Page 182
Publication
Paris,: Gauthier-Villars,
1874-76.
Subject terms
Calculus

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"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.
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