A Treatise on Differential Equations. Supplementary VolumeMacmillan, 1865 - 235 σελίδες |
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Σελίδα 6
... Eliminate between these equations f ( x , y ) , and we have - dA , dA = 0 . dA , dA dx dy dy dx 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 = 0 . dA , dA dx dy dy dx Therefore , by Prop . I. , A , is a function of A ,, so that the solution reduced to the form ( 32 ) contains but the single arbitrary ...
Σελίδα 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 .
Σελίδα 48
... Eliminating da , da2 dan dx ' dx dx we have a relation between x , a ,, a , ... an ; and this relation , with the given complete ... eliminate a , a ,, ... a ,, and to obtain a rela- tion of the form ( x , y , dy d'y dx ' dx2 d - y = 0 ...
... Eliminating da , da2 dan dx ' dx dx we have a relation between x , a ,, a , ... an ; and this relation , with the given complete ... eliminate a , a ,, ... a ,, and to obtain a rela- tion of the form ( x , y , dy d'y dx ' dx2 d - y = 0 ...
Σελίδα 49
... variation of a and b be such as to satisfy the conditions + 2a dx a ) da + ( x + 26 ) do db = 0 dx ( 8 ) . da db x + = 0 dx da B. D. E. II . 4 da Eliminating hence db and we have dx dx x2 ART . 1. ] 49 ADDITIONS TO CHAPTER X.
... variation of a and b be such as to satisfy the conditions + 2a dx a ) da + ( x + 26 ) do db = 0 dx ( 8 ) . da db x + = 0 dx da B. D. E. II . 4 da Eliminating hence db and we have dx dx x2 ART . 1. ] 49 ADDITIONS TO CHAPTER X.
Σελίδα 50
George Boole Isaac Todhunter. da Eliminating hence db and we have dx dx 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 2 dy + x ) dy - ( 1 + x2 ) y ...
George Boole Isaac Todhunter. da Eliminating hence db and we have dx dx 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 2 dy + x ) dy - ( 1 + x2 ) y ...
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Algebra arbitrary constants Calculus of Variations Cambridge Chap Chapter Christ's College cloth College complete primitive condition Conic Sections contains Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dF dp dp dx dp dq dp dy dq dp du₂ dx dx dx dy dx₁ dx² dy dp dy dx dy dy dy dz dz dy dz dz eliminate English equa expression Extra fcap factor fcap function Geometry given equation Grammar Hence homogeneous function Last Multiplier Latin linear partial differential m₁ Mathematical method ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole proposition reduced relation represent result Schools Second Edition singular solution theorem theory tion transformation Trigonometry u₁ values vanish x₁ Y₁ аф
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