A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 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 ...
Página 20
... Proposition . PROPOSITION . If a relation which makes infinite satisfy dp 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 infinite satisfy dp 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 ...
Página 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 ...
Página 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 QU . du 0 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 QU . du 0 v ...
Página 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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Términos y frases comunes
arbitrary constants Cambridge Chap Chapter College complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dF dF dp dF dx dFdF differential coefficients dp dF dp dp dx dp dq dp dy dp₁ dq dp dv dv dx dp dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor function given equation Hence J. P. MAHAFFY Jacobi Last Multiplier linear partial differential m₁ memoir ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole reduced represent result revised School shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence X₁ Y₁ аф
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