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 K , the function u reduces to a constant v . Then we have U - v C 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 K , the function u reduces to a constant v . Then we have U - v C k - K ...
Página 5
... arbitrary constant . 5. It is proved in Art . 3 , Chap . II . , that the constants . x , y , 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 . x , y , 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 a1 , a ,, ... an no longer as constants but as functions of x , so to be deter- mined as to leave the expressions for y1 , Ya , ... Y as ...
... arbitrary constants of the solution . If we differentiate ( 2 ) with respect to x , regarding a1 , a ,, ... an no longer as constants but as functions of x , so to be deter- mined as to leave the expressions for y1 , Ya , ... Y 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
¹º arbitrary constants Calculus of Variations Chap Chapter common integral complete primitive condition Crelle's Journal deduce derived determine dF dF dF dF dp dF dx dFdF differential coefficients dp dF dp dp dx dp dq dp dy dq dp du₁ du₂ dv dv dx dp dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dq dy dx dy dz dz dx eliminate equa exact differential expression factor given equation Hence homogeneous function independent variables infinite Jacobi Last Multiplier linear partial differential m₁ memoir obtain ordinary differential equations P₁ partial differential equations particular integral Professor Boole proposition reduced represent respect result shewn singular solution suppose system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence x₁ y₁ аф
Pasajes populares
Página viii - On Simultaneous Differential Equations of the First Order in which the Number of the Variables exceeds by more than one the Number of the Equations, 1862, pages 437. ..454. On the Differential 'Equations of Dynamics. A sequel to a Paper on Simultaneous Differential Equations, 1863, pages 485.
Página 146 - ... second degree ; 2ndly that this system may be resolved into four systems, each consisting of two partial differential equations of the first order and first degree, two of which systems are irrelevant and the other two relevant ; Srdly that the solution of the two relevant systems ultimately depends on the solution of a system of ordinary differential equations of the first order, and that from these ordinary differential equations the given equation of the second order may be deduced independently...
Página 74 - On simultaneous differential equations of the first order in which the number of the variables exceeds by more than one the number of the equations,