A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 10
... singular solution is of the form x = constant . be no singular solutions except such as df ( x , c ) = 0 , and such as are found from dc = Similarly , if the complete primitive be expressed in the form xy , c ) , there can be no ...
... singular solution is of the form x = constant . be no singular solutions except such as df ( x , c ) = 0 , and such as are found from dc = Similarly , if the complete primitive be expressed in the form xy , c ) , there can be no ...
Página 11
... singular solution . Substituting it in the com- plete primitive we get y = c , which confirms this . Second . Let y = 0. This satisfies the differential equa- tion ; but from the fact that it comes from d dx = ∞ we have no inference ...
... singular solution . Substituting it in the com- plete primitive we get y = c , which confirms this . Second . Let y = 0. This satisfies the differential equa- tion ; but from the fact that it comes from d dx = ∞ we have no inference ...
Página 12
... solution at all it will be a singular solution . " From Art . 8 onwards it seems assumed that a solution for which dy dc = 0 is always to count as a singular solution , even if it should coincide with a particular integral . This does ...
... solution at all it will be a singular solution . " From Art . 8 onwards it seems assumed that a solution for which dy dc = 0 is always to count as a singular solution , even if it should coincide with a particular integral . This does ...
Página 13
... 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 satisfied , the last two are satisfied . The determination of ...
... 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 satisfied , the last two are satisfied . The determination of ...
Página 14
... singular solution ; nor , on the other hand , as an absolute constant , so leading to a particular primitive . Thus the particular primitive y = ecx being given , the condition dy dc gives ecx = = 0 , - whence c is if x be negative ...
... singular solution ; nor , on the other hand , as an absolute constant , so leading to a particular primitive . Thus the particular primitive y = ecx being given , the condition dy dc gives ecx = = 0 , - whence c is if x be negative ...
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Términos y frases comunes
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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