A Treatise on Differential Equations |
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Page 145
... note that the final criteria dy = dc = 0 , dx dc - 0 are in effect analytical expressions of what logicians term con- ditional propositions . The former expresses that if x be assumed constant , y will not vary for an infinitesimal ...
... note that the final criteria dy = dc = 0 , dx dc - 0 are in effect analytical expressions of what logicians term con- ditional propositions . The former expresses that if x be assumed constant , y will not vary for an infinitesimal ...
Page 186
... NOTE . The reader is reminded that in all references to the general con- ditions = ∞ and dp dy d ( ) = the means simply " infinity ” irrespec- dx tively of sign . See General Theorem , Art . 11 . CHAPTER IX . ON DIFFERENTIAL EQUATIONS ...
... NOTE . The reader is reminded that in all references to the general con- ditions = ∞ and dp dy d ( ) = the means simply " infinity ” irrespec- dx tively of sign . See General Theorem , Art . 11 . CHAPTER IX . ON DIFFERENTIAL EQUATIONS ...
Page 223
... note ) . Ex . Given y + 3x dy + 2y ( dy ) + ( x2 + 2y dy ) dy = 0 . dx dx Supposing the above an exact differential , we are by defi- nition permitted to write aʊ = { y y + 3x dy dx 3 + 2y ( dy ) + ( x2 + 2y3 dy ) dy } dæ ... ( 34 ) ...
... note ) . Ex . Given y + 3x dy + 2y ( dy ) + ( x2 + 2y dy ) dy = 0 . dx dx Supposing the above an exact differential , we are by defi- nition permitted to write aʊ = { y y + 3x dy dx 3 + 2y ( dy ) + ( x2 + 2y3 dy ) dy } dæ ... ( 34 ) ...
Page 232
... note by Poisson on page 239 of the edition of 1808 should be consulted ; it relates to the second of the above two propositions . See also Lacroix , Traité du Calcul Diffé- rentiel ... , Tome II . pp . 382 and 390. ] 10. We proceed to ...
... note by Poisson on page 239 of the edition of 1808 should be consulted ; it relates to the second of the above two propositions . See also Lacroix , Traité du Calcul Diffé- rentiel ... , Tome II . pp . 382 and 390. ] 10. We proceed to ...
Page 271
... NOTE . To solve problems like the above , we observe that if RTS , Fig . 4 , represent the given curve rolling on the given line OX , and APC the curve described by the pole P , then taking OX for the axis of x , and putting OM = x , MP ...
... NOTE . To solve problems like the above , we observe that if RTS , Fig . 4 , represent the given curve rolling on the given line OX , and APC the curve described by the pole P , then taking OX for the axis of x , and putting OM = x , MP ...
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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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