A Treatise on Differential Equations, Volumen 1Macmillan, 1865 - 85 páginas |
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Términos y frases comunes
2ndly arbitrary constant arbitrary function C₁ C₂ Chap complete primitive condition corresponding curve d³y deduce degree derived determined differential coefficients dp dq dp dy dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz eliminating envelope species equa equal exact differential expressed finite given equation gives Hence homogeneous functions independent variable infinite integrating factor involving linear equation Mdx+Ndy method multiplying Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation Prop reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose symbolical form Taylor's theorem theorem tion transformation V₂ whence X₁ Y₁ аф
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Página 270 - Find the equation referred to polar co-ordinates of the curve in which the radius vector is equal to m times the length of the portion of the tangent intercepted between the point of contact and a straight line drawn from the pole to meet the tangent at a given angle. 9.
Página 23 - M and N being functions of the variables x and y. In this mode of representation x is regarded as the independent variable and y as the dependent variable. We may, however, regard y as the independent and x as the dependent variable, on which supposition the form of the typical equation will be...
Página vii - The question of the true value and proper place of symbolical methods is undoubtedly of great importance. Their convenient simplicity — their condensed power — must ever constitute their first claim upon attention. I believe however that, in order to form a just estimate, we must consider them in another aspect, viz. as in some sort the visible manifestation of truths relating to the intimate and vital connexion of language with thought — truths of which it may be presumed that we do not yet...