A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 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 + ...
Página 11
... equa- tion ; but from the fact that it comes from d dx = ∞ we have no inference ; from the fact that it does not come from dp d = ∞ we have the inference that it is a particular integral : it dy corresponds to c = 0 . There remains ...
... equa- tion ; but from the fact that it comes from d dx = ∞ we have no inference ; from the fact that it does not come from dp d = ∞ we have the inference that it is a particular integral : it dy corresponds to c = 0 . There remains ...
Página 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 ...
Página 28
... equa- tion is reduced to the form du f dx = ƒ ( x , u ) , then will น du f ( x , u ) 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 ...
... equa- tion is reduced to the form du f dx = ƒ ( x , u ) , then will น du f ( x , u ) 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 ...
Página 33
... to u as if x were constant . The resulting equa- tion cannot be free from x unless C be infinite , and then it 3 B. D. E. II . will evidently not be satisfied unless I du be infinite 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 3 B. D. E. II . will evidently not be satisfied unless I du be infinite ART . 12. ] 33 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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