A Treatise on Differential EquationsMacmillan, 1865 - 496 σελίδες |
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Σελίδα 1
... differential equation ( ax + by + c ) dx + ( a'x + b'y + c ' ) dy = 0. ] But there exists another transformation by which the equa- tion may be reduced to , ( because it may be constructed from ) , an equation in which the variables are ...
... differential equation ( ax + by + c ) dx + ( a'x + b'y + c ' ) dy = 0. ] But there exists another transformation by which the equa- tion may be reduced to , ( because it may be constructed from ) , an equation in which the variables are ...
Σελίδα 6
... by ( 28 ) , we shall find dA . dA , dx 。 + f1 ( x 。, Yo ) = 0 , dy 。 whence in particular dA . dA . + f1 ( xo , Yo ) dyo = = 0 . Eliminate between these equations f ( x , y ) , and we have dA , dA dA , dA - dx dy dy dx . = 0 . Therefore ...
... by ( 28 ) , we shall find dA . dA , dx 。 + f1 ( x 。, Yo ) = 0 , dy 。 whence in particular dA . dA . + f1 ( xo , Yo ) dyo = = 0 . Eliminate between these equations f ( x , y ) , and we have dA , dA dA , dA - dx dy dy dx . = 0 . Therefore ...
Σελίδα 10
... dy dx in the latter case = : 00 , and therefore = 0 , and this dx dy implies that the Thus there can are found from x = constant . singular solution is of the form x = constant . be no singular solutions except such as df ( x , c ) = 0 ...
... dy dx in the latter case = : 00 , and therefore = 0 , and this dx dy implies that the Thus there can are found from x = constant . singular solution is of the form x = constant . be no singular solutions except such as df ( x , c ) = 0 ...
Σελίδα 11
... by supposition we are now investigating what is furnished by dp dy = ∞ Professor Boole met the objection in substance thus : " It will be found that the rules in the book are correct in this case . What is implied in the Chapter ...
... by supposition we are now investigating what is furnished by dp dy = ∞ Professor Boole met the objection in substance thus : " It will be found that the rules in the book are correct in this case . What is implied in the Chapter ...
Σελίδα 12
... by Professor Boole in the above reply , that if dp dy = leads to a solution which does not involve y nothing is to be inferred ... is important . It corrects the state- ment put too strongly in Chap . VIII . Art . 7 , " All we can affirm dp ...
... by Professor Boole in the above reply , that if dp dy = leads to a solution which does not involve y nothing is to be inferred ... is important . It corrects the state- ment put too strongly in Chap . VIII . Art . 7 , " All we can affirm dp ...
Άλλες εκδόσεις - Προβολή όλων
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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