A Treatise on Differential EquationsMacmillan, 1865 - 496 σελίδες |
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Σελίδα 11
... ∞ 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 . There remains the case of x = 0 when n ART . 3. ] 11 ADDITIONS TO CHAPTER VIII .
... ∞ 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 . There remains the case of x = 0 when n ART . 3. ] 11 ADDITIONS TO CHAPTER VIII .
Σελίδα 13
... corresponds to a given value of x . One important remark yet remains . The elimination of c between a primitive y = f ( x , c ) and the derived equation dy dc = 0 , does not necessarily lead to a singular solution in the sense above ...
... corresponds to a given value of x . One important remark yet remains . The elimination of c between a primitive y = f ( x , c ) and the derived equation dy dc = 0 , does not necessarily lead to a singular solution in the sense above ...
Σελίδα 17
... corresponding solution of the differential equation is singular , and is geometrically represented by an envelope of the curves of primitives . But it may be , as we have seen in a particular example , that the relation does not ...
... corresponding solution of the differential equation is singular , and is geometrically represented by an envelope of the curves of primitives . But it may be , as we have seen in a particular example , that the relation does not ...
Σελίδα 23
... correspond- ing exact one by containing a factor which the singular solu- tion makes to vanish . If we knew that factor , we could by rejecting it reduce the given differential equation to a form in which it would no longer be satisfied ...
... correspond- ing exact one by containing a factor which the singular solu- tion makes to vanish . If we knew that factor , we could by rejecting it reduce the given differential equation to a form in which it would no longer be satisfied ...
Σελίδα 32
... corresponding theory of the singular solutions of differential equations has been of very slow growth . The existence of these solutions was first recognised in 1715 by Brook Taylor ; it was scarcely more than recognised by Clairaut in ...
... corresponding theory of the singular solutions of differential equations has been of very slow growth . The existence of these solutions was first recognised in 1715 by Brook Taylor ; it was scarcely more than recognised by Clairaut in ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
¹º arbitrary constants C₂ 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 dP dp dp dx dp dq dp dx dp dy dq dp dv dv dx dF dx dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dq dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor given equation Hence J. P. MAHAFFY Jacobi Last Multiplier linear partial differential m₁ MACMILLAN'S EDUCATIONAL CATALOGUE ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole revised School singular solution theorem theory tion u₁ u₂ values vanish X₁ Y₁ аф
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