A Treatise on Differential Equations, Volumen1Macmillan and Company, 1877 - 496 páginas |
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Página 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 ...
Página 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 ...
Página 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 ...
Página 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 ...
Página 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 У x = C , we have on differentiating and clearing the result of ...
... 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 У x = C , we have on differentiating and clearing the result of ...
Otras ediciones - Ver todas
Términos y frases comunes
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition Crown 8vo curve d²u deduce derived determined differential coefficients dp dq dp dy dv dv dx dx dx dy dx dz dx² dy 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 partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation V₁ V₂ whence X₁ Y₁ аф
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