A Treatise on Differential Equations, Volumen1Macmillan, 1872 - 85 páginas |
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... shewn more conveniently in the preface to the supple- mentary volume , which will soon be published . The present volume then is a reprint of the original Treatise with changes and corrections , some of which were indicated in Professor ...
... shewn more conveniently in the preface to the supple- mentary volume , which will soon be published . The present volume then is a reprint of the original Treatise with changes and corrections , some of which were indicated in Professor ...
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... shewn in the previous section that from an equa- tion containing x and y with an arbitrary constant c , we can by differentiation , and elimination ( if necessary ) of that con- stant , obtain the differential equation of the first ...
... shewn in the previous section that from an equa- tion containing x and y with an arbitrary constant c , we can by differentiation , and elimination ( if necessary ) of that con- stant , obtain the differential equation of the first ...
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... differential equation to its primitive . Considered with reference to these processes the primitive is sometimes termed the final integral . It has been shewn that the order of succession in ART . 7. ] 13 SECOND AND HIGHER ORDERS .
... differential equation to its primitive . Considered with reference to these processes the primitive is sometimes termed the final integral . It has been shewn that the order of succession in ART . 7. ] 13 SECOND AND HIGHER ORDERS .
Página 14
George Boole. It has been shewn that the order of succession in which arbitrary constants are eliminated is indifferent . It may be added , and upon the same ground , that the elimination may be simultaneous . If we write the primitive ...
George Boole. It has been shewn that the order of succession in which arbitrary constants are eliminated is indifferent . It may be added , and upon the same ground , that the elimination may be simultaneous . If we write the primitive ...
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... shewn that two distinct complete primi- tives of Mdx + Ndy = 0 cannot exist . For suppose that there are two such ... shews , by Prop . I , that is a function of u . The second equation is then equivalent to f ( u ) = C , and this is ...
... shewn that two distinct complete primi- tives of Mdx + Ndy = 0 cannot exist . For suppose that there are two such ... shews , by Prop . I , that is a function of u . The second equation is then equivalent to f ( u ) = C , and this is ...
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Términos y frases comunes
2ndly algebraic arbitrary constants arbitrary function assume C₁ C₂ Chap Chapter complete primitive condition Crown 8vo curve deduce derived determined differential coefficients dp dp dp dq dp dy dt dt dv du dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dy dz dz Edition eliminating equa exact differential expressed fcap finite given equation Hence homogeneous functions independent variable integrating factor involving method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral pdx+qdy primitive equation reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation whence X₁ y₁