A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 91
Side vii
... obtained may be particular or general , - they may be defective , wholly or partially , or complete or redundant , in those elements of a solution which are termed arbitrary . If defective , the question arises how the defect . is to be ...
... obtained may be particular or general , - they may be defective , wholly or partially , or complete or redundant , in those elements of a solution which are termed arbitrary . If defective , the question arises how the defect . is to be ...
Side 7
... obtained . The equations xy = sin x , xy sin x + 1 , = are particular solutions of the given differential equation . The term solution is still employed , even when the inte- gration necessary in order to obtain in a finite and explicit ...
... obtained . The equations xy = sin x , xy sin x + 1 , = are particular solutions of the given differential equation . The term solution is still employed , even when the inte- gration necessary in order to obtain in a finite and explicit ...
Side 9
... obtained by mere differentiation and removal of irrelevant factors , i.e. of factors which do not 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 ...
... obtained by mere differentiation and removal of irrelevant factors , i.e. of factors which do not 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 ...
Side 10
... 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 constants being given , if we differentiate twice ...
... 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 constants being given , if we differentiate twice ...
Side 13
... obtained the equation - dy — by = ( a - b ) cea dx ( 12 ) . Differentiating this and eliminating c we again obtain the same final result ( 11 ) . That result is a differential equation of the second order , and ( 8 ) , involving both ...
... obtained the equation - dy — by = ( a - b ) cea dx ( 12 ) . Differentiating this and eliminating c we again obtain the same final result ( 11 ) . That result is a differential equation of the second order , and ( 8 ) , involving both ...
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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