A Treatise on Differential Equations, Τόμος 2Macmillan and Company, 1865 |
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Σελίδα xi
... Propositions in Algebra connected with the Theory of Probabilities . Vol . , 9 , 1855 , pages 165 ... 179 . On a Question in the Theory of Probabilities . By A. Cayley , Esq . [ This paper embodies some observations by Professor Boole ...
... Propositions in Algebra connected with the Theory of Probabilities . Vol . , 9 , 1855 , pages 165 ... 179 . On a Question in the Theory of Probabilities . By A. Cayley , Esq . [ This paper embodies some observations by Professor Boole ...
Σελίδα 20
... Proposition . PROPOSITION . If a relation which makes dp infinite satisfy dy the given differential equation of the first order , but do not satisfy all the higher differential equations obtained from it , such solution will be singular ...
... Proposition . PROPOSITION . If a relation which makes dp infinite satisfy dy the given differential equation of the first order , but do not satisfy all the higher differential equations obtained from it , such solution will be singular ...
Σελίδα 25
... PROPOSITION . If u = 0 be a solution of a differential equation of the first order between y and x , and du = f ( x , u ) dx represent the form which that equation assumes when u and x are assumed as variables instead of y and x , then ...
... PROPOSITION . If u = 0 be a solution of a differential equation of the first order between y and x , and du = f ( x , u ) dx represent the form which that equation assumes when u and x are assumed as variables instead of y and x , then ...
Σελίδα 26
George Boole. In the statement of this proposition x is supposed to be constant in the integration relative to u . The differential equation after the transformation which introduces u and x as variables becomes Let du dx Judu = = QU . v ...
George Boole. In the statement of this proposition x is supposed to be constant in the integration relative to u . The differential equation after the transformation which introduces u and x as variables becomes Let du dx Judu = = QU . v ...
Σελίδα 27
... proposition still remains to be proved . 10. PROPOSITION . If u = 0 be a singular ART . 9. ] 27 ADDITIONS TO CHAPTER VIII .
... proposition still remains to be proved . 10. PROPOSITION . If u = 0 be a singular ART . 9. ] 27 ADDITIONS TO CHAPTER VIII .
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Συχνά εμφανιζόμενοι όροι και φράσεις
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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