A Treatise on Differential EquationsMacmillan, 1865 - 496 σελίδες |
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Σελίδα 7
... obtain an infinite system of such curves , each consisting of two branches . The aggregate of branches thus obtained is evidently the same as the aggre- gate of curves given by the two primitives ( 5 ) and ( 6 ) , un- restricted by any ...
... obtain an infinite system of such curves , each consisting of two branches . The aggregate of branches thus obtained is evidently the same as the aggre- gate of curves given by the two primitives ( 5 ) and ( 6 ) , un- restricted by any ...
Σελίδα 8
... obtain every form of solution which is implied either in the func- tional equation ( F ) , or in its component primitives = V11 , V2 = C. , Vn = Cn . 1 2 The same considerations justify us in speaking of ( 15 ) as the complete primitive ...
... obtain every form of solution which is implied either in the func- tional equation ( F ) , or in its component primitives = V11 , V2 = C. , Vn = Cn . 1 2 The same considerations justify us in speaking of ( 15 ) as the complete primitive ...
Σελίδα 10
... obtained would involve x only , while it is a condition accompanying the use of dp dy = ∞ that it leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and furnish a ...
... obtained would involve x only , while it is a condition accompanying the use of dp dy = ∞ that it leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and furnish a ...
Σελίδα 18
... obtained above . The first , though it does not determine c as a function of x , still ex- presses a relation between c and x , which is the ground of the fulfilment of the condition dp SS dy = ∞ We may further notice a peculiarity ...
... obtained above . The first , though it does not determine c as a function of x , still ex- presses a relation between c and x , which is the ground of the fulfilment of the condition dp SS dy = ∞ We may further notice a peculiarity ...
Σελίδα 20
... , but do not satisfy all the higher differential equations obtained from it , such solution will be singular and of the envelope species . Ex . 1. By comparison with its complete primitive we 20 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
... , but do not satisfy all the higher differential equations obtained from it , such solution will be singular and of the envelope species . Ex . 1. By comparison with its complete primitive we 20 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
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Συχνά εμφανιζόμενοι όροι και φράσεις
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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