A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 2
... arbitrary constant and u a function of x , y , and constants which are not arbitrary . Suppose too that when one of these constants k assumes a particular value ê , the function u reduces to a constant v . Then we have U - v C k - K = k ...
... arbitrary constant and u a function of x , y , and constants which are not arbitrary . Suppose too that when one of these constants k assumes a particular value ê , the function u reduces to a constant v . Then we have U - v C k - K = k ...
Página 5
... arbitrary constant . 5. It is proved in Art . 3 , Chap . II . , that the constants xo , yo , initial values of the variables x , y in the solution of the differential equation of the first order , are necessarily equivalent to one arbitrary ...
... arbitrary constant . 5. It is proved in Art . 3 , Chap . II . , that the constants xo , yo , initial values of the variables x , y in the solution of the differential equation of the first order , are necessarily equivalent to one arbitrary ...
Página 8
... arbitrary constants . In a physi- cal or geometrical application we should not only be per- mitted to assign a particular value to the arbitrary constant in ( 15 ) , so deducing what in reference to its source would then be termed a ...
... arbitrary constants . In a physi- cal or geometrical application we should not only be per- mitted to assign a particular value to the arbitrary constant in ( 15 ) , so deducing what in reference to its source would then be termed a ...
Página 46
... arbitrary constants of the solution . If we differentiate ( 2 ) with respect to x , regarding a , a ,, ... an no longer as constants but as functions of x , so to be deter- mined as to leave the expressions for y1 , Y2 , ... Yn as ...
... arbitrary constants of the solution . If we differentiate ( 2 ) with respect to x , regarding a , a ,, ... an no longer as constants but as functions of x , so to be deter- mined as to leave the expressions for y1 , Y2 , ... Yn as ...
Página 48
... constants . The differential equation of the ( n - 1 ) th order thus obtained has an integral expressing y in terms ... arbitrary constants which they contain . A solu- tion containing n - 1 arbitrary constants is called by 48 [ CH ...
... constants . The differential equation of the ( n - 1 ) th order thus obtained has an integral expressing y in terms ... arbitrary constants which they contain . A solu- tion containing n - 1 arbitrary constants is called by 48 [ CH ...
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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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