A Treatise on Differential Equations |
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Page 7
... primitives ( 5 ) and ( 6 ) . And it is only in this sense not general that it groups these relations together in a particular manner . To the expression of the complete primitive a certain variety of form may be given without affecting ...
... primitives ( 5 ) and ( 6 ) . And it is only in this sense not general that it groups these relations together in a particular manner . To the expression of the complete primitive a certain variety of form may be given without affecting ...
Page 8
... complete primitive of the differential equation given , and which in geometry represents the same totality of branches of curves as ( 9 ) , with this difference only , that they are differ- ently paired together . 2. [ This Article ...
... complete primitive of the differential equation given , and which in geometry represents the same totality of branches of curves as ( 9 ) , with this difference only , that they are differ- ently paired together . 2. [ This Article ...
Page 10
... complete primitive be expressed in the form x = F ( y , c ) , there can be no singular solutions except dF ( y , c ) such as are found from from y = = constant . dc = 0 , and such as are found In Art . 8 of Chapter VIII . we read , " We ...
... complete primitive be expressed in the form x = F ( y , c ) , there can be no singular solutions except dF ( y , c ) such as are found from from y = = constant . dc = 0 , and such as are found In Art . 8 of Chapter VIII . we read , " We ...
Page 13
... complete primitive аф = 2 √x2 + y2 - - У dy dx - x = 0 m2 — y — c = 0 . - do = Here dy - √2 + 3 --1 , de - √ Hence √x2 y2 - do d - 1 . dc dy √ x2 + y2 — m2 = m2 dc √x2 + y2 — m2 y - dy dx Both and dc dc - vanish then if dx x √x2 ...
... complete primitive аф = 2 √x2 + y2 - - У dy dx - x = 0 m2 — y — c = 0 . - do = Here dy - √2 + 3 --1 , de - √ Hence √x2 y2 - do d - 1 . dc dy √ x2 + y2 — m2 = m2 dc √x2 + y2 — m2 y - dy dx Both and dc dc - vanish then if dx x √x2 ...
Page 14
... primitives , nor strictly one of those curves . It represents a curve formed of branches from two of them . It is most fitly characterized as a particular primitive marked by a sin- gularity in the mode of its derivation from the complete ...
... primitives , nor strictly one of those curves . It represents a curve formed of branches from two of them . It is most fitly characterized as a particular primitive marked by a sin- gularity in the mode of its derivation from the complete ...
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Common terms and phrases
¹º arbitrary constants C₂ 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 dP dp dp dx dp dq dp dx dp dy dq dp dv dv dx dF dx dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dq dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor given equation Hence J. P. MAHAFFY Jacobi Last Multiplier linear partial differential m₁ MACMILLAN'S EDUCATIONAL CATALOGUE ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole revised School singular solution theorem theory tion u₁ u₂ values vanish X₁ Y₁ аф
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