A Treatise on Differential Equations, Volume 1 |
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Page xiii
... Second member a function of x , -Variation Dependent class , 203 , Properties of linear Analogy with Algebraic equations , 206. Exer- member is 0 , 200 . of parameters , ib . equations , 204 , cises , 207 . CHAPTER X. EQUATIONS OF AN ...
... Second member a function of x , -Variation Dependent class , 203 , Properties of linear Analogy with Algebraic equations , 206. Exer- member is 0 , 200 . of parameters , ib . equations , 204 , cises , 207 . CHAPTER X. EQUATIONS OF AN ...
Page 4
... two following equations , in addition to those already given , will exemplify ... second degree and under a radical sign . In ( 5 ) we meet with the second ... member . 3. Differential Equations are ranked in order and degree according ...
... two following equations , in addition to those already given , will exemplify ... second degree and under a radical sign . In ( 5 ) we meet with the second ... member . 3. Differential Equations are ranked in order and degree according ...
Page 6
... second member X are either constant quantities or functions of the indepen- dent variable a only , the equation is said to be linear . Equa- tions ( 1 ) , ( 2 ) and ( 3 ) are thus seen to be linear , but ( 4 ) and ( 5 ) are not linear ...
... second member X are either constant quantities or functions of the indepen- dent variable a only , the equation is said to be linear . Equa- tions ( 1 ) , ( 2 ) and ( 3 ) are thus seen to be linear , but ( 4 ) and ( 5 ) are not linear ...
Page 24
... two vari- ables x and y . Then , if V be expressible as a function of v , the condition dV dv dV dv dx dy dy dx = 0 ( 1 ) ... second member vanishes independently both of the form of v as a function of x and y , and of the form of Vas a ...
... two vari- ables x and y . Then , if V be expressible as a function of v , the condition dV dv dV dv dx dy dy dx = 0 ( 1 ) ... second member vanishes independently both of the form of v as a function of x and y , and of the form of Vas a ...
Page 26
... second member of this equation being a function of x and y , since M and N are functions of those variables , we may ... II . DIFFERENTIAL EQUATIONS OF THE.
... second member of this equation being a function of x and y , since M and N are functions of those variables , we may ... II . DIFFERENTIAL EQUATIONS OF THE.
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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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