A Treatise on Differential Equations |
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Page 2
... И k - บ С - v k K - K Now the second member being a function of an arbitrary constant is equivalent to an arbitrary constant and may be replaced by C. The first member is a vanishing fraction 2 [ CH . XIX . ADDITIONS TO CHAPTER II .
... И k - บ С - v k K - K Now the second member being a function of an arbitrary constant is equivalent to an arbitrary constant and may be replaced by C. The first member is a vanishing fraction 2 [ CH . XIX . ADDITIONS TO CHAPTER II .
Page 3
George Boole. replaced by C. The first member is a vanishing fraction , the limiting value of which is ( du ) , the brackets being used to denote that after the differentiation k is to be made equal to x . Hence the solution becomes du ...
George Boole. replaced by C. The first member is a vanishing fraction , the limiting value of which is ( du ) , the brackets being used to denote that after the differentiation k is to be made equal to x . Hence the solution becomes du ...
Page 13
... vanish then if dc - x2 + y2 — m2 = 0 . " This therefore is the singular solution and it satisfies both the tests , as both x and y are contained in its expression . Of the partial tests do аф аф = 0 , = ∞ , = ∞ , dc dx dy the first is ...
... vanish then if dc - x2 + y2 — m2 = 0 . " This therefore is the singular solution and it satisfies both the tests , as both x and y are contained in its expression . Of the partial tests do аф аф = 0 , = ∞ , = ∞ , dc dx dy the first is ...
Page 14
... vanish , and the nume- rator of ( 9 ) , instead of being the difference of a finite and an infinite quantity , would be the difference of two infinite and equal quantities . [ See Chap . VIII . Art . 8. ] It would not there- fore be ...
... vanish , and the nume- rator of ( 9 ) , instead of being the difference of a finite and an infinite quantity , would be the difference of two infinite and equal quantities . [ See Chap . VIII . Art . 8. ] It would not there- fore be ...
Page 23
... vanish with y . We can therefore neither affirm nor deny that the proposed solution is of the envelope species . 8. Before demonstrating a general Rule for the discrimi- nation of solutions of this character , we shall notice certain of ...
... vanish with y . We can therefore neither affirm nor deny that the proposed solution is of the envelope species . 8. Before demonstrating a general Rule for the discrimi- nation of solutions of this character , we shall notice certain of ...
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¹º Algebra arbitrary constants BROOKE FOSS WESTCOTT Calculus of Variations Cambridge Chap Chapter cloth College complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dF dp dp dx dp dq dp dy dq dp du₁ dx dp dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz EDUCATIONAL BOOKS eliminate equa expression factor Fcap function given equation Hence Jacobi Last Multiplier linear partial differential m₁ Mathematical obtain ordinary differential equations P₁ partial differential equations particular integral Professor Boole proposition reduced represent result shewn singular solution system of ordinary theorem theory tion transformation Trigonometry u₁ U₂ values vanish whence X₁ Y₁ аф
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