A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 93
Side xi
... 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. Solution by development , 41. Exercises , 44 ...
... 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. Solution by development , 41. Exercises , 44 ...
Side xiii
... complete primitive , 141 . General theorem , 148. Geometrical interpretation , 152. Deri- vation of the singular solution from the differential equation , 153 . More general definition of singular solution , 163. Distinction of species ...
... complete primitive , 141 . General theorem , 148. Geometrical interpretation , 152. Deri- vation of the singular solution from the differential equation , 153 . More general definition of singular solution , 163. Distinction of species ...
Side xiv
... Complete primitive , general primitive , and singular solution , 339. Sufficiency of a single complete pri- mitive , 345. Singular solutions , 346. Geometrical applica- tions , 347. Symmetrical and more general solution of equations of ...
... Complete primitive , general primitive , and singular solution , 339. Sufficiency of a single complete pri- mitive , 345. Singular solutions , 346. Geometrical applica- tions , 347. Symmetrical and more general solution of equations of ...
Side 8
... complete primitive . The relation ( 14 ) in- volving the arbitrary constant c is virtually the complete primitive of the differential equation ( 13 ) . It will be observed that the terms ' general solution ' and ' complete primitive ...
... complete primitive . The relation ( 14 ) in- volving the arbitrary constant c is virtually the complete primitive of the differential equation ( 13 ) . It will be observed that the terms ' general solution ' and ' complete primitive ...
Side 9
... complete primitive . That primitive might have been so prepared as to lead to the same final equation by mere differentiation . Thus , re- ducing the primitive to the form y 3 = 0 , x we have on differentiating and clearing the result ...
... complete primitive . That primitive might have been so prepared as to lead to the same final equation by mere differentiation . Thus , re- ducing the primitive to the form y 3 = 0 , x we have on differentiating and clearing the result ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
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