A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 7
... consisting of two branches , and giving to every possible value we obtain an infinite system of such curves , each consisting of two branches . The aggregate of branches thus obtained is evidently the same as the aggre- gate of curves ...
... consisting of two branches , and giving to every possible value we obtain an infinite system of such curves , each consisting of two branches . The aggregate of branches thus obtained is evidently the same as the aggre- gate of curves ...
Página 23
... consists of y multiplied by a rational and entire func- tion of logy . It is easy to see that all the higher differential coefficients of y hence derived will possess the same character . And all such vanish with y . We can therefore ...
... consists of y multiplied by a rational and entire func- tion of logy . It is easy to see that all the higher differential coefficients of y hence derived will possess the same character . And all such vanish with y . We can therefore ...
Página 25
... consist in that the transformed equation is of the form du dx = QU , in which while Q neither vanishes nor becomes infinite when u = 0 , the functions U and du a fate 0 both vanish with u . The question whether U is of the form u as ...
... consist in that the transformed equation is of the form du dx = QU , in which while Q neither vanishes nor becomes infinite when u = 0 , the functions U and du a fate 0 both vanish with u . The question whether U is of the form u as ...
Página 34
... consists in the comparison of differential coefficients , and he supposes it universal . He adopts the hypothesis of his predecessors as to the forms of expansion , but with some recognition of its insufficiency . Lagrange in the ...
... consists in the comparison of differential coefficients , and he supposes it universal . He adopts the hypothesis of his predecessors as to the forms of expansion , but with some recognition of its insufficiency . Lagrange in the ...
Página 41
... consisting of z , and differential coefficients of z multiplied by known functions of x . The result of substitution of these values in the given differential equation will therefore consist also of two classes of terms , viz . terms ...
... consisting of z , and differential coefficients of z multiplied by known functions of x . The result of substitution of these values in the given differential equation will therefore consist also of two classes of terms , viz . terms ...
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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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