A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
Inni boken
Resultat 1-5 av 80
Side 8
... elimination of c between it and the primitive will lead to the differential equation in question . Thus if the complete primitive be y = = ∞ . ( 1 ) , · we have on differentiation , dy dx = C and 8 [ CH . I. GENESIS OF DIFFERENTIAL ...
... elimination of c between it and the primitive will lead to the differential equation in question . Thus if the complete primitive be y = = ∞ . ( 1 ) , · we have on differentiation , dy dx = C and 8 [ CH . I. GENESIS OF DIFFERENTIAL ...
Side 9
George Boole. we have on differentiation , dy dx = C and , eliminating the constant c , dy y = x dx . ( 2 ) , . ( 3 ) , the differential equation of the first order of which ( 1 ) is the complete primitive . That primitive might have ...
George Boole. we have on differentiation , dy dx = C and , eliminating the constant c , dy y = x dx . ( 2 ) , . ( 3 ) , the differential equation of the first order of which ( 1 ) is the complete primitive . That primitive might have ...
Side 10
... elimination ( if necessary ) of that con- stant , obtain the differential equation of the first order , of which the given equation constitutes the complete primitive . In like manner an equation connecting x , y , and two arbitrary ...
... elimination ( if necessary ) of that con- stant , obtain the differential equation of the first order , of which the given equation constitutes the complete primitive . In like manner an equation connecting x , y , and two arbitrary ...
Side 11
... eliminating b between these equations , y = = X dy dx - ax2 ( 6 ) , a differential equation of the first order free from the constant b . Differentiating this equation we have x d'y dx2 = 2ax , and , eliminating a between the last two ...
... eliminating b between these equations , y = = X dy dx - ax2 ( 6 ) , a differential equation of the first order free from the constant b . Differentiating this equation we have x d'y dx2 = 2ax , and , eliminating a between the last two ...
Side 12
... elimination , & c . applied thereto can only serve , either 1st , to bring out or manifest the dependence above referred to , or 2ndly , to modify the accidental form of its expression ; but in no sense to create such dependence or ...
... elimination , & c . applied thereto can only serve , either 1st , to bring out or manifest the dependence above referred to , or 2ndly , to modify the accidental form of its expression ; but in no sense to create such dependence or ...
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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