A Treatise on Differential Equations. Supplementary Volume |
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Page 7
... consisting of two branches , and giving to C 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 C 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 ...
Page 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 ...
Page 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 f . 0 du U 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 f . 0 du U both vanish with u . The question whether U is of the form u as ...
Page 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 ...
Page 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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Common terms and phrases
Algebra arbitrary constants Calculus of Variations Cambridge Chap Chapter Christ's College cloth College complete primitive condition Conic Sections contains Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dF dp dp dx dp dq dp dy dq dp du₂ dx dx dx dy dx₁ dx² dy dp dy dx dy dy dy dz dz dy dz dz eliminate English equa expression Extra fcap factor fcap function Geometry given equation Grammar Hence homogeneous function Last Multiplier Latin linear partial differential m₁ Mathematical method ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole proposition reduced relation represent result Schools Second Edition singular solution theorem theory tion transformation Trigonometry u₁ values vanish x₁ Y₁ аф
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