A Treatise on Differential Equations, Volumen1Macmillan and Company, 1877 - 496 páginas |
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Página 5
... dy dy dx + a = dx b , is of the first order and of the second degree . The equation day dy + a + by2 = c , dx2 dx is of the second order and of the first degree . The equation dy = √ ( 3 - xdy ) reduced to the rational form 2 dy dy + x ...
... dy dy dx + a = dx b , is of the first order and of the second degree . The equation day dy + a + by2 = c , dx2 dx is of the second order and of the first degree . The equation dy = √ ( 3 - xdy ) reduced to the rational form 2 dy dy + x ...
Página 6
... day dy +5 da dx - ( 1 − x2 ) dzy dx2 - 8y = sin x , dy XC + 4y = cos x , dx the former of which is a linear differential equation with constant coefficients , while the latter would be described as a linear differential equation with ...
... day dy +5 da dx - ( 1 − x2 ) dzy dx2 - 8y = sin x , dy XC + 4y = cos x , dx the former of which is a linear differential equation with constant coefficients , while the latter would be described as a linear differential equation with ...
Página 12
... dy day & c . Thus to a given abscissa of a result for y , x ' dæ2 ' given curve , i.e. of a curve determined as to its species by the form of its equation , and as to its elements by the values of the constants in that equation ...
... dy day & c . Thus to a given abscissa of a result for y , x ' dæ2 ' given curve , i.e. of a curve determined as to its species by the form of its equation , and as to its elements by the values of the constants in that equation ...
Página 14
... dy ¤1 ( x , y , dx ' C2 C3 Cn ) = 0 . Differentiating this equation with respect to x , and regarding dy y and as functions of that quantity , we obtain directly , or dx by elimination of c2 , an equation of the second order of the ...
... dy ¤1 ( x , y , dx ' C2 C3 Cn ) = 0 . Differentiating this equation with respect to x , and regarding dy y and as functions of that quantity , we obtain directly , or dx by elimination of c2 , an equation of the second order of the ...
Página 16
... dy , the differential equations of the dx ' first order must have originated in the same primitive . Fur- dy thermore , that primitive will be obtained by eliminating dx between the two differential equations given . Ex . The ...
... dy , the differential equations of the dx ' first order must have originated in the same primitive . Fur- dy thermore , that primitive will be obtained by eliminating dx between the two differential equations given . Ex . The ...
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Términos y frases comunes
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition Crown 8vo curve d²u deduce derived determined differential coefficients dp dq dp dy dv dv dx dx dx dy dx dz dx² dy dy dx dy dz dz dx dz dz Edition eliminating equa exact differential expressed Extra fcap fcap finite given equation Hence homogeneous functions Illustrations independent variable infinite integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation V₁ V₂ whence X₁ Y₁ аф
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