A Treatise on Differential EquationsMacmillan, 1865 - 496 σελίδες |
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Σελίδα 1
... relations equivalent to the following , viz .: The quantities m1 , m , are roots of the quadratic 2 am2 − ( b + a ' ) m + b ' = 0 . - The quantities A , A ' , C , C ' are determined by the system of equations A + A ' = a , Am1 + A'm2 ...
... relations equivalent to the following , viz .: The quantities m1 , m , are roots of the quadratic 2 am2 − ( b + a ' ) m + b ' = 0 . - The quantities A , A ' , C , C ' are determined by the system of equations A + A ' = a , Am1 + A'm2 ...
Σελίδα 4
... relation between y and x is regarded as one of pure magnitude , and the interpreta- tion of the differential equation becomes a limiting case of that of the equation of finite differences ( Eq . ( 3 ) , Chap . 11. ) . But if we ...
... relation between y and x is regarded as one of pure magnitude , and the interpreta- tion of the differential equation becomes a limiting case of that of the equation of finite differences ( Eq . ( 3 ) , Chap . 11. ) . But if we ...
Σελίδα 5
... relation connecting x and y may be shewn thus . Let y = ( x 。, Yo , x ) be the relation between x and y indicated by the supposed motion , x , y , being the initial point of departure . Then this point being on the line of motion , x ...
... relation connecting x and y may be shewn thus . Let y = ( x 。, Yo , x ) be the relation between x and y indicated by the supposed motion , x , y , being the initial point of departure . Then this point being on the line of motion , x ...
Σελίδα 7
... relations between y and x which are deducible from the original primitives ( 5 ) and ( 6 ) . And it is only in this sense not general that it groups these relations together in a particular manner . C2 . To the expression of the ...
... relations between y and x which are deducible from the original primitives ( 5 ) and ( 6 ) . And it is only in this sense not general that it groups these relations together in a particular manner . C2 . To the expression of the ...
Σελίδα 10
... relation obtained would involve x only , while it is a condition accompanying the use of dp dy = ∞ that it leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and ...
... relation obtained would involve x only , while it is a condition accompanying the use of dp dy = ∞ that it leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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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