A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 2
... C k - K = k - v -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 .
... C k - K = k - v -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 .
Página 3
George Boole. replaced by C. The first member is a vanishing fraction , the the brackets being used to limiting value of which is ( du ) , the brackets denote that after the differentiation k is to be made equal to ê . Hence the solution ...
George Boole. replaced by C. The first member is a vanishing fraction , the the brackets being used to limiting value of which is ( du ) , the brackets denote that after the differentiation k is to be made equal to ê . Hence the solution ...
Página 13
... vanish then if dc de 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 do = 0 , = ∞ = ∞ dc dx dy the first is not ...
... vanish then if dc de 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 do = 0 , = ∞ = ∞ dc dx dy the first is not ...
Página 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 ...
Página 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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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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