A Treatise on Differential Equations, Volume 1 |
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Page vii
... operations . I have endeavoured to shew in Chap . XVI . , that the expressions by which these inverse operations are sym- bolized are in reality a species of interrogations , admitting of answers , legitimate , but differing in species ...
... operations . I have endeavoured to shew in Chap . XVI . , that the expressions by which these inverse operations are sym- bolized are in reality a species of interrogations , admitting of answers , legitimate , but differing in species ...
Page 27
... operation , a series of values of y will be deter- mined , only one of which is arbitrary , while all the others are assigned in terms of that arbitrary value and of the known values of x . If , for example , we have the particular ...
... operation , a series of values of y will be deter- mined , only one of which is arbitrary , while all the others are assigned in terms of that arbitrary value and of the known values of x . If , for example , we have the particular ...
Page 42
... , y ) + Y , ( an , y ) ƒ , ( x , y ) . 2 dx dy And , continuing thus to repeat the same operation , we obtain a series of equations determining the successive differential coefficients of 42 [ CH . II . GENERAL SOLUTION BY DEVELOPMENT .
... , y ) + Y , ( an , y ) ƒ , ( x , y ) . 2 dx dy And , continuing thus to repeat the same operation , we obtain a series of equations determining the successive differential coefficients of 42 [ CH . II . GENERAL SOLUTION BY DEVELOPMENT .
Page 381
... operations themselves are represented . du d dx Thus is written symbolically in the form u , the dx sym- d bol denoting an operation of which u is the subject . In dx thus expressing an operation by a symbol , in studying the laws of ...
... operations themselves are represented . du d dx Thus is written symbolically in the form u , the dx sym- d bol denoting an operation of which u is the subject . In dx thus expressing an operation by a symbol , in studying the laws of ...
Page 382
... operation is repeated , the number of times which it is understood to be performed is expressed by an index attached to the symbol of operation . Thus d dx 2 d d ( ~ + a ) u = ( 1 + a ) ( 2 + a ) u dx dx • d'u du dx2 dx = + 2a + a3u ...
... operation is repeated , the number of times which it is understood to be performed is expressed by an index attached to the symbol of operation . Thus d dx 2 d d ( ~ + a ) u = ( 1 + a ) ( 2 + a ) u dx dx • d'u du dx2 dx = + 2a + a3u ...
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Common terms and phrases
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition corresponding Crown 8vo curve deduce degree derived determined differential coefficients dp dy dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition eliminating equa exact differential expressed Extra fcap fcap finite given equation Hence homogeneous functions Illustrations independent variable infinite integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew singular solution substituting suppose Taylor's theorem theorem tion transformation V₁ whence y₁ аф
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