A Treatise on Differential Equations. Supplementary Volume |
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Page 1
... equa- tion may be reduced to , ( because it may be constructed from ) , an equation in which the variables are separated . Assume as this equation and let ( Ay ' + C ) dx ' + ( A'x ' + C ' ) dy ' = 0 ............... . ( 1 ) x ' = x + ...
... equa- tion may be reduced to , ( because it may be constructed from ) , an equation in which the variables are separated . Assume as this equation and let ( Ay ' + C ) dx ' + ( A'x ' + C ' ) dy ' = 0 ............... . ( 1 ) x ' = x + ...
Page 11
... equa- tion ; but from the fact that it comes from d dx ( 1 ) = ∞ we have no inference ; from the fact that it does not come from dp dy we have the inference that it is a particular integral : it corresponds to c = 0 . - 1 There remains ...
... equa- tion ; but from the fact that it comes from d dx ( 1 ) = ∞ we have no inference ; from the fact that it does not come from dp dy we have the inference that it is a particular integral : it corresponds to c = 0 . - 1 There remains ...
Page 27
... equa- tion which it does satisfy , merely by writing therein for its expression as a function of x and y . It cannot therefore be a case of the complete primitive in any sense . It must be a singular solution of the envelope species ...
... equa- tion which it does satisfy , merely by writing therein for its expression as a function of x and y . It cannot therefore be a case of the complete primitive in any sense . It must be a singular solution of the envelope species ...
Page 28
... equa- tion is reduced to the form then will du = f ( x , u ) , dx du become 0 when u = = 0 . Let the complete primitive be represented by F ( x , u ) = C , then , since dF ( x , u ) , dF ( x , u ) du + da 0 , du dx we have if for ...
... equa- tion is reduced to the form then will du = f ( x , u ) , dx du become 0 when u = = 0 . Let the complete primitive be represented by F ( x , u ) = C , then , since dF ( x , u ) , dF ( x , u ) du + da 0 , du dx we have if for ...
Page 33
... to u as if x were constant . The resulting equa- tion cannot be free from x unless C be infinite , and then it B. D. E. II . 3 du I will evidently not be satisfied unless ( x ART . 12. ] 33 ADDITIONS TO CHAPTER VIII . *
... to u as if x were constant . The resulting equa- tion cannot be free from x unless C be infinite , and then it B. D. E. II . 3 du I will evidently not be satisfied unless ( x ART . 12. ] 33 ADDITIONS TO CHAPTER VIII . *
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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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