A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Side vi
... gives occasion to new applications of deductive reasoning ; but those applications may be only possible through the methods and the processes which belong to an earlier stage . Thus , to take an illustration from the subject of the ...
... gives occasion to new applications of deductive reasoning ; but those applications may be only possible through the methods and the processes which belong to an earlier stage . Thus , to take an illustration from the subject of the ...
Side 2
... differential coefficients , with or without the primitive variables from which those differential coefficients are derived . That which gives to the study of differential equations its 2 [ CH . I. OF THE NATURE AND ORIGIN.
... differential coefficients , with or without the primitive variables from which those differential coefficients are derived . That which gives to the study of differential equations its 2 [ CH . I. OF THE NATURE AND ORIGIN.
Side 3
George Boole. That which gives to the study of differential equations its peculiar value , is the circumstance that many of the most im- portant conceptions of Geometry and Mechanics can only be realized in thought by means of the ...
George Boole. That which gives to the study of differential equations its peculiar value , is the circumstance that many of the most im- portant conceptions of Geometry and Mechanics can only be realized in thought by means of the ...
Side 10
... gives rise to the differential equation of the first order dy dx - ay = 0 , while the equation immediately derived from it by differ- dy entiation , viz . = cae , has for its complete primitive dx y = ce * + c ' . To the last mentioned ...
... gives rise to the differential equation of the first order dy dx - ay = 0 , while the equation immediately derived from it by differ- dy entiation , viz . = cae , has for its complete primitive dx y = ce * + c ' . To the last mentioned ...
Side 16
... gives rise to the same differential equation of the second order , of which the original equation constitutes the ... give the same value of dx2 dy as a function of x , y , and the differential equations of the dx ' first order must have ...
... gives rise to the same differential equation of the second order , of which the original equation constitutes the ... give the same value of dx2 dy as a function of x , y , and the differential equations of the dx ' first order must have ...
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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