A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα 7
... result is termed the solution , or , still more definitely , the general solution of the equation . It involves an arbitrary constant , c , by giving particular values to which a series of particular solutions is obtained . The ...
... result is termed the solution , or , still more definitely , the general solution of the equation . It involves an arbitrary constant , c , by giving particular values to which a series of particular solutions is obtained . The ...
Σελίδα 8
George Boole. and the last result is called the solution of the given equation , although it involves an integration which cannot be performed in finite terms . The relation among the variables which constitutes the general solution of a ...
George Boole. and the last result is called the solution of the given equation , although it involves an integration which cannot be performed in finite terms . The relation among the variables which constitutes the general solution of a ...
Σελίδα 9
... result of fractions , x dy dx -y = 0 , which agrees with ( 3 ) . And generally , if a primitive involving an arbitrary constant c be reduced to the form ( x , y ) = c , the corresponding differential equation will be obtained by mere ...
... result of fractions , x dy dx -y = 0 , which agrees with ( 3 ) . And generally , if a primitive involving an arbitrary constant c be reduced to the form ( x , y ) = c , the corresponding differential equation will be obtained by mere ...
Σελίδα 11
... result would have been arrived at if the order of the eliminations had been reversed . Thus , if a be eliminated between ( 4 ) and ( 5 ) , we shall have dy dx Ꮳ + bx - 2y = 0 , a differential equation of the first order , different in ...
... result would have been arrived at if the order of the eliminations had been reversed . Thus , if a be eliminated between ( 4 ) and ( 5 ) , we shall have dy dx Ꮳ + bx - 2y = 0 , a differential equation of the first order , different in ...
Σελίδα 12
... result for y , d ' da dy d2y & c . Thus to a given abscissa of a 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 ...
... result for y , d ' da dy d2y & c . Thus to a given abscissa of a 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 ...
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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