A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 40
... depend upon only one unknown quantity , viz . z . It remains then to deter- mine z . For this purpose we must complete the expression of the differential coefficients of y , and substitute in the given dif- ferential equation , and then ...
... depend upon only one unknown quantity , viz . z . It remains then to deter- mine z . For this purpose we must complete the expression of the differential coefficients of y , and substitute in the given dif- ferential equation , and then ...
Página 74
... the present Chapter . Connexion of the Systems . 2. PROP . I. The solution of a system of simultaneous linear partial differential equations of the first order may be made to depend upon that of a system of ordinary ( 74 ) [ CH . XXV .
... the present Chapter . Connexion of the Systems . 2. PROP . I. The solution of a system of simultaneous linear partial differential equations of the first order may be made to depend upon that of a system of ordinary ( 74 ) [ CH . XXV .
Página 75
George Boole. made to depend upon that of a system of ordinary differential equations of the first order in which the number of the vari- ables exceeds by more than one the number of the equations . The system of partial differential ...
George Boole. made to depend upon that of a system of ordinary differential equations of the first order in which the number of the vari- ables exceeds by more than one the number of the equations . The system of partial differential ...
Página 87
... depends on the solution of a system of ordinary differential equations reduci- ble to the exact form . This does not mean that each equation of the system is reducible to the exact form , but that the equations may be combined together ...
... depends on the solution of a system of ordinary differential equations reduci- ble to the exact form . This does not mean that each equation of the system is reducible to the exact form , but that the equations may be combined together ...
Página 93
... depend upon that of an ordinary differential equation of the ( -1 ) th degree between the two variables ( ~ -1 ) and p . For we have do ' _ " афш - 2 ) dom - 2 ) ( 4-1 ) = аф do p ' аф φ ' døm − 1 ) __ ƒ ( $ , $ ' , ............ . plu ...
... depend upon that of an ordinary differential equation of the ( -1 ) th degree between the two variables ( ~ -1 ) and p . For we have do ' _ " афш - 2 ) dom - 2 ) ( 4-1 ) = аф do p ' аф φ ' døm − 1 ) __ ƒ ( $ , $ ' , ............ . plu ...
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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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