A Treatise on Differential Equations, Opseg 2Macmillan and Company, 1865 |
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Stranica 4
... equation of finite differences ( Eq . ( 3 ) , Chap . II . ) . But if we represent x and y by the rectangular co - ordinates of a moving point on a plane the differential equation 4 [ CH . XIX . ADDITIONS TO CHAPTER II .
... equation of finite differences ( Eq . ( 3 ) , Chap . II . ) . But if we represent x and y by the rectangular co - ordinates of a moving point on a plane the differential equation 4 [ CH . XIX . ADDITIONS TO CHAPTER II .
Stranica 7
... represent a curve 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 ...
... represent a curve 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 ...
Stranica 14
... represent an envelope of the curves of particu- lar primitives , nor strictly one of those curves . It represents a curve formed of branches from two of them . It is most fitly characterized as a particular primitive marked by a sin ...
... represent an envelope of the curves of particu- lar primitives , nor strictly one of those curves . It represents a curve formed of branches from two of them . It is most fitly characterized as a particular primitive marked by a sin ...
Stranica 19
... represent the envelopes of curves of primi- tives , or shall be extended to all solutions which , satisfying the indicate the existence of a relation be- dp condition = 8 , dy tween c and x , and possess an actual singularity arising ...
... represent the envelopes of curves of primi- tives , or shall be extended to all solutions which , satisfying the indicate the existence of a relation be- dp condition = 8 , dy tween c and x , and possess an actual singularity arising ...
Stranica 23
... represent the given singular solution of the dif ferential equation by u = 0 , u being a given function of x and y . Then introducing u and x instead of y and x as variables , the ART . 8. ] . 23 ADDITIONS TO CHAPTER VIII .
... represent the given singular solution of the dif ferential equation by u = 0 , u being a given function of x and y . Then introducing u and x instead of y and x as variables , the ART . 8. ] . 23 ADDITIONS TO CHAPTER VIII .
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Uobičajeni izrazi i fraze
arbitrary constants C₂ Chap Chapter cloth common integral complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dp dx dp dq dp dy dp₁ dq dp du₁ dx dp dx dx dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz eliminate equa expression Extra fcap factor Fcap given equation Heir of Redclyffe Hence HENRY KINGSLEY homogeneous function independent variables infinite Jacobi JAMES MCCOSH Last Multiplier linear partial differential m₁ memoir obtain ordinary differential equations P₁ partial differential equation particular integral Professor Boole proposition reduced represent result Second Edition shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence x₁ Y₁ аф
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