A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 44
Side 1
... connected by a known relation , e . g . the ordinate and abscissa of a given curve , it defines the rate of variation of the one , y , as referred to that of the other , x , by means of the fundamental con- ception of a limit ; it ...
... connected by a known relation , e . g . the ordinate and abscissa of a given curve , it defines the rate of variation of the one , y , as referred to that of the other , x , by means of the fundamental con- ception of a limit ; it ...
Side 10
... connecting x , y , and two arbitrary constants being given , if we differentiate twice , and eliminate , should they not have already disappeared , the arbitrary constants , we shall arrive at a differential equation of the second order ...
... connecting x , y , and two arbitrary constants being given , if we differentiate twice , and eliminate , should they not have already disappeared , the arbitrary constants , we shall arrive at a differential equation of the second order ...
Side 23
... connecting x and y , I shall first establish a prelimi- nary proposition expressing the condition of mutual depend- ence of functions of two variables ; I shall then ( 23 ) CHAPTER II ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND ...
... connecting x and y , I shall first establish a prelimi- nary proposition expressing the condition of mutual depend- ence of functions of two variables ; I shall then ( 23 ) CHAPTER II ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND ...
Side 31
... connected by a relation C = sin C , which is independent of the variables x and y . And in general the test of the accordance of two solutions of a differential equation , each involving an arbitrary constant , is , that on eliminating ...
... connected by a relation C = sin C , which is independent of the variables x and y . And in general the test of the accordance of two solutions of a differential equation , each involving an arbitrary constant , is , that on eliminating ...
Side 88
... connected with the subject of the present Chapter , is dis- cussed in the Supplementary Volume , Chapter XXXI . ] EXERCISES . 1. The following equations admit of integrating factors of the form ( x ) , viz . ( 1 ) ( x2 + y2 + 2x ) dx + ...
... connected with the subject of the present Chapter , is dis- cussed in the Supplementary Volume , Chapter XXXI . ] EXERCISES . 1. The following equations admit of integrating factors of the form ( x ) , viz . ( 1 ) ( x2 + y2 + 2x ) dx + ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
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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