A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 53
Side vii
... admitting of answers , legitimate , but differing in species and character ac- cording to the nature of the transformations to which the expressions from which they are derived have been subjected . The solutions thus obtained may be ...
... admitting of answers , legitimate , but differing in species and character ac- cording to the nature of the transformations to which the expressions from which they are derived have been subjected . The solutions thus obtained may be ...
Side xiv
... admitting a first integral of the form u = f ( v ) , 362. Deduction of such integral when possible , 364. Relations of first integrals , 366. General rule , 369. Miscellaneous theorems . Poisson's method , 375 . Duality , 376 ...
... admitting a first integral of the form u = f ( v ) , 362. Deduction of such integral when possible , 364. Relations of first integrals , 366. General rule , 369. Miscellaneous theorems . Poisson's method , 375 . Duality , 376 ...
Side 19
... admits of no such limitation . Monge has deduced the general differential equation of lines of the second order expressed by the algebraic equation ax2 + bxy + cy2 + ex + fy = 1 . It is 3 9 ( de ) d'y - 45 2-2 ART . 11. ] 19 GEOMETRICAL ...
... admits of no such limitation . Monge has deduced the general differential equation of lines of the second order expressed by the algebraic equation ax2 + bxy + cy2 + ex + fy = 1 . It is 3 9 ( de ) d'y - 45 2-2 ART . 11. ] 19 GEOMETRICAL ...
Side 24
... admits readily of finite solution ; and I shall lastly deduce its general solution in a series . PROP . 1. Let V and v be explicit functions of the two vari- ables x and y . Then , if V be expressible as a function of v , the condition ...
... admits readily of finite solution ; and I shall lastly deduce its general solution in a series . PROP . 1. Let V and v be explicit functions of the two vari- ables x and y . Then , if V be expressible as a function of v , the condition ...
Side 29
... admits of finite solution . 4. The equation Mdx + Ndy = 0 can always be solved when the variables in M and N admit of being separated ; i.e. when the equation can be reduced to the form Xdx + Ydy = 0 .. ( 8 ) , in which X is a function ...
... admits of finite solution . 4. The equation Mdx + Ndy = 0 can always be solved when the variables in M and N admit of being separated ; i.e. when the equation can be reduced to the form Xdx + Ydy = 0 .. ( 8 ) , in which X is a function ...
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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