A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 91
Side 7
... arbitrary constant , c , by giving particular values to which a series of particular solutions is obtained . The equations xy = sin x , xy sin x + 1 , = are particular solutions of the given differential equation . The term solution is ...
... arbitrary constant , c , by giving particular values to which a series of particular solutions is obtained . The equations xy = sin x , xy sin x + 1 , = are particular solutions of the given differential equation . The term solution is ...
Side 8
... arbitrary constant c . Differentiating on the supposition that x is the independent variable , we obtain a new equation which must involved , and which may involve dx ' any or all of the quantities x , y and c . If it do not involve c ...
... arbitrary constant c . Differentiating on the supposition that x is the independent variable , we obtain a new equation which must involved , and which may involve dx ' any or all of the quantities x , y and c . If it do not involve c ...
Side 9
... arbitrary constant c be reduced to the form ( x , y ) = c , the corresponding differential equation will be obtained by mere differentiation and removal of irrelevant factors , i.e. of factors which do not contain dy , and do not ...
... arbitrary constant c be reduced to the form ( x , y ) = c , the corresponding differential equation will be obtained by mere differentiation and removal of irrelevant factors , i.e. of factors which do not contain dy , and do not ...
Side 10
... arbitrary , the value which it bears in the primitive being determined by ... constant c , we can by differentiation , and elimination ( if necessary ) of ... arbitrary constants being given , if we differentiate twice , and eliminate ...
... arbitrary , the value which it bears in the primitive being determined by ... constant c , we can by differentiation , and elimination ( if necessary ) of ... arbitrary constants being given , if we differentiate twice , and eliminate ...
Side 11
... constant b . Differentiating this equation we have x d'y dx2 = 2ax , and ... constants are eliminated does not affect the form of the final differential ... arbitrary constants consists only in this , that it is thus made to stand as ...
... constant b . Differentiating this equation we have x d'y dx2 = 2ax , and ... constants are eliminated does not affect the form of the final differential ... arbitrary constants consists only in this , that it is thus made to stand as ...
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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