A Treatise on Differential Equations, Τόμος 2Macmillan and Company, 1865 |
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Σελίδα 13
... of c between a primitive y = f ( x , c ) and the derived equation dy cc = 0 , does not necessarily lead to a singular solution in the = sense above explained . For it is possible that the ART . 4. ] 13 ADDITIONS TO CHAPTER VIII .
... of c between a primitive y = f ( x , c ) and the derived equation dy cc = 0 , does not necessarily lead to a singular solution in the = sense above explained . For it is possible that the ART . 4. ] 13 ADDITIONS TO CHAPTER VIII .
Σελίδα 14
... derived from the condition d.x dc -- = 0 . 5. We have seen that the equation dy = 0 may be satisfied dc by an absolutely constant value of c , so leading to a particu- lar primitive and not a singular solution . In this case ( x + h , c ) ...
... derived from the condition d.x dc -- = 0 . 5. We have seen that the equation dy = 0 may be satisfied dc by an absolutely constant value of c , so leading to a particu- lar primitive and not a singular solution . In this case ( x + h , c ) ...
Σελίδα 15
George Boole. term , i . e . for a solution derived from the complete primitive by giving to c an absolutely constant value . This is one point of contrast between the conditions dy de = = 0 , dp dy = ထ There is another not less ...
George Boole. term , i . e . for a solution derived from the complete primitive by giving to c an absolutely constant value . This is one point of contrast between the conditions dy de = = 0 , dp dy = ထ There is another not less ...
Σελίδα 16
... derived from the complete primitive by giving to c a variable value will , if it involve y in its expres- sion , satisfy the condition dp = 8 ; dy and if it involve x , the relation d -- = 8 . dx But relations satisfying these ...
... derived from the complete primitive by giving to c a variable value will , if it involve y in its expres- sion , satisfy the condition dp = 8 ; dy and if it involve x , the relation d -- = 8 . dx But relations satisfying these ...
Σελίδα 20
... derived from the differential equation , are the same as those derived from the complete primitive . But a solution deduced from the condition constructed so as to yield the same value of dp = ∞ is only dy dy as the given dx ...
... derived from the differential equation , are the same as those derived from the complete primitive . But a solution deduced from the condition constructed so as to yield the same value of dp = ∞ is only dy dy as the given dx ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
arbitrary constants C₂ Chap Chapter cloth common integral complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dp dx dp dq dp dy dp₁ dq dp du₁ dx dp dx dx dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz eliminate equa expression Extra fcap factor Fcap given equation Heir of Redclyffe Hence HENRY KINGSLEY homogeneous function independent variables infinite Jacobi JAMES MCCOSH Last Multiplier linear partial differential m₁ memoir obtain ordinary differential equations P₁ partial differential equation particular integral Professor Boole proposition reduced represent result Second Edition shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence x₁ Y₁ аф
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