A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
Inni boken
Resultat 1-5 av 30
Side vii
... considered . And here the necessity of some prior acquaintance with the things themselves , rather than with the symbolic forms of their ex- pression , must become apparent . The most accomplished in the use of symbols must sometimes ...
... considered . And here the necessity of some prior acquaintance with the things themselves , rather than with the symbolic forms of their ex- pression , must become apparent . The most accomplished in the use of symbols must sometimes ...
Side 13
... equation to its primitive . Considered with reference to these processes the primitive is sometimes termed the final integral . It has been shewn that the order of succession in ART . 7. ] 13 SECOND AND HIGHER ORDERS .
... equation to its primitive . Considered with reference to these processes the primitive is sometimes termed the final integral . It has been shewn that the order of succession in ART . 7. ] 13 SECOND AND HIGHER ORDERS .
Side 47
... considered in the previous Chapter under which the equation Mdx + Ndy = 0 is integrable by the sepa- ration of the variables , are but a small number of the cases in which a solution expressible in finite terms exists , Analysts have ...
... considered in the previous Chapter under which the equation Mdx + Ndy = 0 is integrable by the sepa- ration of the variables , are but a small number of the cases in which a solution expressible in finite terms exists , Analysts have ...
Side 84
... considered in Art . 6 , viz . = 0 .......... ( 24 ) , P1dx + P2dy + Q ( xdy — ydx ) = 0 ... - P1 and P , being homogeneous of the degree p , and Q homo- geneous of the degree q . y y Q = Let P1 = x2 + ( ~ ) , P , - ~ ↓ ) , 2 - x ...
... considered in Art . 6 , viz . = 0 .......... ( 24 ) , P1dx + P2dy + Q ( xdy — ydx ) = 0 ... - P1 and P , being homogeneous of the degree p , and Q homo- geneous of the degree q . y y Q = Let P1 = x2 + ( ~ ) , P , - ~ ↓ ) , 2 - x ...
Side 88
... considered is virtually only a limited case of the general equation ( 21 ) . If we assume it becomes y + c = s , R - 2c = t , ( s + t ) ds + cc'tdt + c ́t ( tds — sdt ) , - which evidently falls under that equation . [ The Jacobian ...
... considered is virtually only a limited case of the general equation ( 21 ) . If we assume it becomes y + c = s , R - 2c = t , ( s + t ) ds + cc'tdt + c ́t ( tds — sdt ) , - which evidently falls under that equation . [ The Jacobian ...
Andre utgaver - Vis alle
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