A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα xiv
... variables , 286. Equations of an order higher than the first , 289. Exercises , 291 . CHAPTER XIII . SIMULTANEOUS DIFFERENTIAL EQUATIONS . Meaning of a determinate system , 292. General theory of simulta- neous equations of the first ...
... variables , 286. Equations of an order higher than the first , 289. Exercises , 291 . CHAPTER XIII . SIMULTANEOUS DIFFERENTIAL EQUATIONS . Meaning of a determinate system , 292. General theory of simulta- neous equations of the first ...
Σελίδα 1
... variable quantities x and y connected by a known relation , e . g . the ordinate and abscissa of a given curve , it ... variables , x , y , & c . which is sought . In that branch of the Integral Calculus with which the student B. D. E. ...
... variable quantities x and y connected by a known relation , e . g . the ordinate and abscissa of a given curve , it ... variables , x , y , & c . which is sought . In that branch of the Integral Calculus with which the student B. D. E. ...
Σελίδα 2
... variables . All these including ( 1 ) are examples of differential equations . The essential character consists in the presence of differential coefficients . The equations d'y dy +2 = 0 ..... dx dx . ( 2 ) , x2 day + x dy dx2 + y = sin ...
... variables . All these including ( 1 ) are examples of differential equations . The essential character consists in the presence of differential coefficients . The equations d'y dy +2 = 0 ..... dx dx . ( 2 ) , x2 day + x dy dx2 + y = sin ...
Σελίδα 3
... variable . 2ndly . Partial differential equations , characterized by the presence of partial differential coefficients , and therefore in- dicating the existence of two or more independent variables with respect to which those ...
... variable . 2ndly . Partial differential equations , characterized by the presence of partial differential coefficients , and therefore in- dicating the existence of two or more independent variables with respect to which those ...
Σελίδα 4
... variable x , the dependent variable dy dx and the differential coefficient are all involved ; but , dy while in the previous examples appears only in the first dx degree , in the present one it appears in the second degree and under a ...
... variable x , the dependent variable dy dx and the differential coefficient are all involved ; but , dy while in the previous examples appears only in the first dx degree , in the present one it appears in the second degree and under a ...
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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