A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα 11
... which the primitive derives from the presence of its arbitrary constants consists only in this , that it is thus made to stand as the , representative of an infinite number of particular equations , ART . 7. ] 11 SECOND AND HIGHER ORDERS .
... which the primitive derives from the presence of its arbitrary constants consists only in this , that it is thus made to stand as the , representative of an infinite number of particular equations , ART . 7. ] 11 SECOND AND HIGHER ORDERS .
Σελίδα 12
George Boole. , representative of an infinite number of particular equations , in each of which these constants receive particular and definite values . If in any one of the equations thus particularized we further give to x a definite ...
George Boole. , representative of an infinite number of particular equations , in each of which these constants receive particular and definite values . If in any one of the equations thus particularized we further give to x a definite ...
Σελίδα 18
George Boole. two , it is formally more correct to regard them as infinite in number , but as so related that any two of them which are independent contain by implication all the rest . Such considerations are easily extended to ...
George Boole. two , it is formally more correct to regard them as infinite in number , but as so related that any two of them which are independent contain by implication all the rest . Such considerations are easily extended to ...
Σελίδα 44
... infinite we must revert to the previous form , and give to x such a value as will render the coefficients finite , and therefore justify the application of Taylor's theorem . Virtually the integral ( 30 ) involves like ( 31 ) only one ...
... infinite we must revert to the previous form , and give to x such a value as will render the coefficients finite , and therefore justify the application of Taylor's theorem . Virtually the integral ( 30 ) involves like ( 31 ) only one ...
Σελίδα 56
... infinite number of integrating factors , all of which are included under a single functional expression . It has been shewn , Chap . II . Art . 2 , that the above equa- tion always involves the existence of a complete primitive of the ...
... infinite number of integrating factors , all of which are included under a single functional expression . It has been shewn , Chap . II . Art . 2 , that the above equa- tion always involves the existence of a complete primitive of the ...
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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