A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 45
Side vii
... derived have been subjected . The solutions thus obtained may be particular or general , - they may be defective , wholly or partially , or complete or redundant , in those elements of a solution which are termed arbitrary . If ...
... derived have been subjected . The solutions thus obtained may be particular or general , - they may be defective , wholly or partially , or complete or redundant , in those elements of a solution which are termed arbitrary . If ...
Side viii
... derived from those of the direct processes to which they stand related ; in point of expediency it is recommended by the greater simplicity , and even in some instances by the greater generality , of the demonstrations to which it leads ...
... derived from those of the direct processes to which they stand related ; in point of expediency it is recommended by the greater simplicity , and even in some instances by the greater generality , of the demonstrations to which it leads ...
Side 2
... differential coefficients , with or without the primitive variables from which those differential coefficients are derived . That which gives to the study of differential equations its 2 [ CH . I. OF THE NATURE AND ORIGIN.
... differential coefficients , with or without the primitive variables from which those differential coefficients are derived . That which gives to the study of differential equations its 2 [ CH . I. OF THE NATURE AND ORIGIN.
Side 7
... x dy da - ^ ! — x € 2 = 0 ......... ...... we should thence derive in succession xdu de da y IC -- x2 dx Jeda - x + c x ( 13 ) , ( 14 ) , } and the last result is called the solution of the ART . 5. ] GENERAL SOLUTION .
... x dy da - ^ ! — x € 2 = 0 ......... ...... we should thence derive in succession xdu de da y IC -- x2 dx Jeda - x + c x ( 13 ) , ( 14 ) , } and the last result is called the solution of the ART . 5. ] GENERAL SOLUTION .
Side 8
... derived , not only with their primitive , but with each other , which need a distinct elucidation . Suppose that the complete primitive expresses a relation between x , y and an arbitrary constant c . Differentiating on the supposition ...
... derived , not only with their primitive , but with each other , which need a distinct elucidation . Suppose that the complete primitive expresses a relation between x , y and an arbitrary constant c . Differentiating on the supposition ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
2ndly algebraic arbitrary constants arbitrary function assume C₁ C₂ Chap Chapter complete primitive condition Crown 8vo curve deduce derived determined differential coefficients dp dp dp dq dp dy dt dt dv du dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dy dz dz Edition eliminating equa exact differential expressed fcap finite given equation Hence homogeneous functions independent variable integrating factor involving method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral pdx+qdy primitive equation reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation whence X₁ y₁