A Treatise on Differential EquationsMacmillan, 1865 - 496 sider |
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Resultat 1-5 av 53
Side 6
... Eliminate between these equations f ( x , y ) , and we have dA , dA dA , dA - dx dy dy dx . = 0 . Therefore , by Prop . I. , A , is a function of A. , so that the solution reduced to the form ( 32 ) contains but the single arbitrary ...
... Eliminate between these equations f ( x , y ) , and we have dA , dA dA , dA - dx dy dy dx . = 0 . Therefore , by Prop . I. , A , is a function of A. , so that the solution reduced to the form ( 32 ) contains but the single arbitrary ...
Side 13
... elimination of c between a primitive y = f ( x , c ) and the derived equation dy = 0 , does not necessarily lead to a singular solution in the dc sense above explained . For it is possible that the ART . 4. ] 13 ADDITIONS TO CHAPTER VIII .
... elimination of c between a primitive y = f ( x , c ) and the derived equation dy = 0 , does not necessarily lead to a singular solution in the dc sense above explained . For it is possible that the ART . 4. ] 13 ADDITIONS TO CHAPTER VIII .
Side 48
... Eliminating da , da , 1 dan dx dx da " " we have a relation between x , a , a , ... an ; and this relation , with ... eliminate a , a ,, ... a ,, and to obtain a rela- tion of the form + ( x , y , dy , dy , dry ) ... n - 1 = This is a ...
... Eliminating da , da , 1 dan dx dx da " " we have a relation between x , a , a , ... an ; and this relation , with ... eliminate a , a ,, ... a ,, and to obtain a rela- tion of the form + ( x , y , dy , dy , dry ) ... n - 1 = This is a ...
Side 49
... the variation of a and b be such as to satisfy the conditions da db + 2a ) + ( x + 2b ) = 0 di ( 8 ) . da + dx ✺ | 8 db 0 dx B. D. E. II . 4 da db Eliminating hence and dx dx ' we have ART . 1. ] 49 ADDITIONS TO CHAPTER X.
... the variation of a and b be such as to satisfy the conditions da db + 2a ) + ( x + 2b ) = 0 di ( 8 ) . da + dx ✺ | 8 db 0 dx B. D. E. II . 4 da db Eliminating hence and dx dx ' we have ART . 1. ] 49 ADDITIONS TO CHAPTER X.
Side 50
George Boole. da db Eliminating hence and dx dx ' we have x2 2a - -2bx = 0 . 2 And from this , the complete primitive , and the first of the derived equations ( 7 ) eliminating a and b , we find ( d2 ) 2 + ( x2 + x ) dy − ( 1 + x2 ) y ...
George Boole. da db Eliminating hence and dx dx ' we have x2 2a - -2bx = 0 . 2 And from this , the complete primitive , and the first of the derived equations ( 7 ) eliminating a and b , we find ( d2 ) 2 + ( x2 + x ) dy − ( 1 + x2 ) y ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
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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