A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα v
... contain that kind of matter which has usually been thought suitable for the beginner , while the latter ones are devoted either to an account of recent discovery , or to the discussion of such deeper questions of principle as are likely ...
... contain that kind of matter which has usually been thought suitable for the beginner , while the latter ones are devoted either to an account of recent discovery , or to the discussion of such deeper questions of principle as are likely ...
Σελίδα 2
... contain , the primitive vari- ables . And thus we are led to the following definition . DEF . A differential equation is an expressed relation in- volving differential coefficients , with or without the primitive variables from which ...
... contain , the primitive vari- ables . And thus we are led to the following definition . DEF . A differential equation is an expressed relation in- volving differential coefficients , with or without the primitive variables from which ...
Σελίδα 9
... contain dy , and do not therefore affect dy dx dx ' the relation in which stands to x and y . For it is in that relation , as already intimated , Art . 2 , that the essential character of the differential equation consists . It is to be ...
... contain dy , and do not therefore affect dy dx dx ' the relation in which stands to x and y . For it is in that relation , as already intimated , Art . 2 , that the essential character of the differential equation consists . It is to be ...
Σελίδα 10
... containing x and y with an arbitrary constant c , we can by differentiation , and elimination ( if necessary ) of that con- stant , obtain the differential equation of the first order , of which the given equation constitutes the ...
... containing x and y with an arbitrary constant c , we can by differentiation , and elimination ( if necessary ) of that con- stant , obtain the differential equation of the first order , of which the given equation constitutes the ...
Σελίδα 15
... containing n arbitrary constants there belong n differential equations of the first order , each involving n - 1 arbitrary constants . But as those differential equations are all formed by mere pro- eesses of elimination from two ...
... containing n arbitrary constants there belong n differential equations of the first order , each involving n - 1 arbitrary constants . But as those differential equations are all formed by mere pro- eesses of elimination from two ...
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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