A Treatise on Differential Equations. Supplementary Volume |
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Page 7
... obtain an infinite system of such curves , each consisting of two branches . The aggregate of branches thus obtained is evidently the same as the aggre- gate of curves given by the two primitives ( 5 ) and ( 6 ) , un- restricted by any ...
... obtain an infinite system of such curves , each consisting of two branches . The aggregate of branches thus obtained is evidently the same as the aggre- gate of curves given by the two primitives ( 5 ) and ( 6 ) , un- restricted by any ...
Page 8
... obtain every form of solution which is implied either in the func- tional equation ( F ) , or in its component primitives V1 = c1 , V2 = C2 , V2 = Cn . 1 C2 ... 22 The same considerations justify us in speaking of ( 15 ) as the complete ...
... obtain every form of solution which is implied either in the func- tional equation ( F ) , or in its component primitives V1 = c1 , V2 = C2 , V2 = Cn . 1 C2 ... 22 The same considerations justify us in speaking of ( 15 ) as the complete ...
Page 10
... obtained would involve x only , while it is a condition accompanying the use of co that it leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and furnish a solution ...
... obtained would involve x only , while it is a condition accompanying the use of co that it leads to solutions involving y at least . " It is ob- jected , Why may we pass over this case ? Such a case might occur and furnish a solution ...
Page 18
... obtained above . The first , though it does not determine c as a function of x , still ex- presses a relation between c and x , which is the ground of the fulfilment of the condition dp dy = 8 . We e may further notice a peculiarity ...
... obtained above . The first , though it does not determine c as a function of x , still ex- presses a relation between c and x , which is the ground of the fulfilment of the condition dp dy = 8 . We e may further notice a peculiarity ...
Page 20
... , but do not satisfy all the higher differential equations obtained from it , such solution will be singular and of the envelope species . Ex . 1. By comparison with its complete primitive we 20 [ CII . XXI . ADDITIONS TO CHAPTER VIII .
... , but do not satisfy all the higher differential equations obtained from it , such solution will be singular and of the envelope species . Ex . 1. By comparison with its complete primitive we 20 [ CII . XXI . ADDITIONS TO CHAPTER VIII .
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Algebra arbitrary constants Calculus of Variations Cambridge Chap Chapter Christ's College cloth College complete primitive condition Conic Sections contains Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dF dp dp dx dp dq dp dy dq dp du₂ dx dx dx dy dx₁ dx² dy dp dy dx dy dy dy dz dz dy dz dz eliminate English equa expression Extra fcap factor fcap function Geometry given equation Grammar Hence homogeneous function Last Multiplier Latin linear partial differential m₁ Mathematical method ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole proposition reduced relation represent result Schools Second Edition singular solution theorem theory tion transformation Trigonometry u₁ values vanish x₁ Y₁ аф
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