A Treatise on Differential Equations, Τόμος 2Macmillan and Company, 1865 |
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Σελίδα 9
... may be made more obvious . These remarks will occupy the next Article . 3. The two pages beginning with " And these conditions are sufficient , " and ending with " do not lead to conflicting results , " forming part of Arts . 3 and.
... may be made more obvious . These remarks will occupy the next Article . 3. The two pages beginning with " And these conditions are sufficient , " and ending with " do not lead to conflicting results , " forming part of Arts . 3 and.
Σελίδα 10
... leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and furnish a solution , and then we should want to know the character of that solution . Take for example dy and p ...
... leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and furnish a solution , and then we should want to know the character of that solution . Take for example dy and p ...
Σελίδα 11
... leads to a solution which does not involve y in its expression , nothing is to be inferred whether it is singular or not . Then the proper test is d dy = ∞ . dx In this example we have dp = ∞ gives x " : = ∞ ; no inference ; dy d ...
... leads to a solution which does not involve y in its expression , nothing is to be inferred whether it is singular or not . Then the proper test is d dy = ∞ . dx In this example we have dp = ∞ gives x " : = ∞ ; no inference ; dy d ...
Σελίδα 12
... 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 is that if = gives a solution at all it will be a ...
... 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 is that if = gives a solution at all it will be a ...
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 .
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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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