A Treatise on Differential Equations |
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Page xi
... VARIABLES General equation Mdx + Ndy = 0 , 23. Complete primitive ƒ ( x , y ) = c , 26 . Geometrical illustration , 28. Various integrable cases , 29. Ho- mogeneous equations , 34. Linear equations of first order , 38 . Other forms , 40 ...
... VARIABLES General equation Mdx + Ndy = 0 , 23. Complete primitive ƒ ( x , y ) = c , 26 . Geometrical illustration , 28. Various integrable cases , 29. Ho- mogeneous equations , 34. Linear equations of first order , 38 . Other forms , 40 ...
Page 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 ...
Page 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. ...
Page 2
... variables . All these including ( 1 ) are examples of differential equations . The essential character consists in the presence of differential coefficients . dy dy +2 = 0 da dx The equations 202 day dy + x dx2 dx + y = sin x ( 2 ) ...
... variables . All these including ( 1 ) are examples of differential equations . The essential character consists in the presence of differential coefficients . dy dy +2 = 0 da dx The equations 202 day dy + x dx2 dx + y = sin x ( 2 ) ...
Page 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 ...
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2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter cloth complete primitive condition Crown 8vo curve deduce determined differential coefficients dp dq dp dy dt dt dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition EDUCATIONAL BOOKS elementary eliminating equa exact differential example expressed fcap finite given equation gives Hence homogeneous functions independent variable integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation problem reduced relation represent respect result satisfied second member second order shew singular solution substituting suppose theorem tion transformation TREATISE whence X₁ Y₁ аф
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