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An Elementary Treatise On Partial Differential Equations Designed for the Use O

Cover An Elementary Treatise On Partial Differential Equations Designed for the Use O
An Elementary Treatise On Partial Differential Equations Designed for the Use O
Sir George Biddell Airy
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If T*- a 7y = *« XaM ' M W) = i{Z) ' and the equation is immediately reduced to the form already treated.
If the first side is € (x) x -z a x f (y) x ~, let -^ -, >j and ^ - ^ and the equation is reduced to the sarne form.
d^j efe r f \ dz x dz dx dx * '. ' cfo/ ^' and the equation becomes dx dy In reference to physical investigations, the theory of Partial Differential Equations of the first order is princi- pally valuable as introductory to that of the second order. In this view, it is hoped
...that the instances here given are sufficient.
SIMPLEST EQUATION OF THE SECOND ORDER. 21 TREATMENT OF THE SIMPLEST PARTIAL DIFFERENTIAL EQUATION OF THE SECOND ORDER.
30. The simplest Partial Differential Equation of the second order is d?z — — — = 0. Dx . Dy Integrating with respect to x, and remarking that, by virtue of the reasoning in Article 19, there must be added to the integral an undetermined function of y, f-fto Integrating this with respect to y, and remarking that, for the same reasons, an undetermined function of x must be added, z = (f> (y) + f (x).


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