A Treatise on Differential EquationsMacmillan, 1865 - 496 sider |
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Side 4
... equation of finite differences ( Eq . ( 3 ) , Chap . 11. ) . 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 . 11. ) . 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 .
Side 7
... represent a curve 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 ...
... represent a curve 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 ...
Side 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 ...
Side 19
... represent the envelopes of curves of primi- tives , or shall be extended to all solutions which , satisfying the o , indicate the existence of a relation be- tween c and x , and possess an actual singularity arising from this source ...
... represent the envelopes of curves of primi- tives , or shall be extended to all solutions which , satisfying the o , indicate the existence of a relation be- tween c and x , and possess an actual singularity arising from this source ...
Side 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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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
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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