A Treatise on Differential Equations, Τόμος 2Macmillan and Company, 1865 |
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Σελίδα 19
... . It stands in close relation to a series of properties of singular solutions which admit of an orderly development . Discrimination of singular solutions of the envelope species . 7. 2-2 ART . 6.1 19 ADDITIONS TO CHAPTER VIII .
... . It stands in close relation to a series of properties of singular solutions which admit of an orderly development . Discrimination of singular solutions of the envelope species . 7. 2-2 ART . 6.1 19 ADDITIONS TO CHAPTER VIII .
Σελίδα 27
... admit of the solution u = 0 . It is obvious however that it is best to assume Q so as to make the subsequent integration for determining plest possible . the sim- It is manifest that a solution which can thus be made to cease to satisfy ...
... admit of the solution u = 0 . It is obvious however that it is best to assume Q so as to make the subsequent integration for determining plest possible . the sim- It is manifest that a solution which can thus be made to cease to satisfy ...
Σελίδα 78
... admits . The theory which removes this difficulty will be developed in the following sections . It will be shewn that a system of linear partial differential equations which admits of solution by the assigning to the dependent variable ...
... admits . The theory which removes this difficulty will be developed in the following sections . It will be shewn that a system of linear partial differential equations which admits of solution by the assigning to the dependent variable ...
Σελίδα 81
... admit of reduction to the form of exact differential equations , the integration of which will enable us to construct the general value of P satisfying the system given . B. D. E. II . 6 1st . Suppose the given system of n equations ...
... admit of reduction to the form of exact differential equations , the integration of which will enable us to construct the general value of P satisfying the system given . B. D. E. II . 6 1st . Suppose the given system of n equations ...
Σελίδα 82
... admitting of the same reduction as to form fol- lowed by the same subsequent process of derivation . And the result of each of these completed steps is to convert the system into one containing one equation more than before ; but ...
... admitting of the same reduction as to form fol- lowed by the same subsequent process of derivation . And the result of each of these completed steps is to convert the system into one containing one equation more than before ; but ...
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arbitrary constants C₂ Chap Chapter cloth common integral complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dp dx dp dq dp dy dp₁ dq dp du₁ dx dp dx dx dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz eliminate equa expression Extra fcap factor Fcap given equation Heir of Redclyffe Hence HENRY KINGSLEY homogeneous function independent variables infinite Jacobi JAMES MCCOSH Last Multiplier linear partial differential m₁ memoir obtain ordinary differential equations P₁ partial differential equation particular integral Professor Boole proposition reduced represent result Second Edition shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence x₁ Y₁ аф
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