A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 1
... deduce a system of 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 ...
... deduce a system of 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 ...
Página 8
... deducing what in reference to its source would then be termed a particular primitive , but to combine the re- sults of different determinations of c together , so as to obtain every form of solution which is implied either in the func ...
... deducing what in reference to its source would then be termed a particular primitive , but to combine the re- sults of different determinations of c together , so as to obtain every form of solution which is implied either in the func ...
Página 20
... deduced from the condition constructed so as to yield the same value of dp = ∞ is only dy dy as the given dx differential equation does . If it be of the envelope species , the curve it represents has in general no continuous contact ...
... deduced from the condition constructed so as to yield the same value of dp = ∞ is only dy dy as the given dx differential equation does . If it be of the envelope species , the curve it represents has in general no continuous contact ...
Página 21
... deduce the character of the solution with- out making use of the complete primitive . From the solution we have d'y dx2 d3y = 0 , = = 0 , & c . ad inf . dx3 But from the differential equation dzy 1 = dx2 ( m - 1 ) y m dy m - 2 dx = = m ...
... deduce the character of the solution with- out making use of the complete primitive . From the solution we have d'y dx2 d3y = 0 , = = 0 , & c . ad inf . dx3 But from the differential equation dzy 1 = dx2 ( m - 1 ) y m dy m - 2 dx = = m ...
Página 35
... deduced from the differential equation in its rational and integral expression , to assume the form . [ The demonstration is given in Chap . VIII . Art . 14. ] day dx This ambiguity of value of is evidently but an expres- sion of the ...
... deduced from the differential equation in its rational and integral expression , to assume the form . [ The demonstration is given in Chap . VIII . Art . 14. ] day dx This ambiguity of value of is evidently but an expres- sion of the ...
Otras ediciones - Ver todas
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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