A Treatise on Differential Equations. Supplementary Volume |
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Page 1
... Assume as this equation and let ( Ay ' + C ) dx ' + ( A'x ' + C ' ) dy ' = 0 ............... . ( 1 ) x ' = x + m1y ... assumed equation the values of x ' and y ' , and comparing with the equation given , we deduce a system of relations ...
... Assume as this equation and let ( Ay ' + C ) dx ' + ( A'x ' + C ' ) dy ' = 0 ............... . ( 1 ) x ' = x + m1y ... assumed equation the values of x ' and y ' , and comparing with the equation given , we deduce a system of relations ...
Page 2
... assumes a particular value κ , the function น reduces to a constant v . Then we have U - v k - K = C - v k - K Now the second member being a function of an arbitrary constant is equivalent to an arbitrary constant and may be replaced by ...
... assumes a particular value κ , the function น reduces to a constant v . Then we have U - v k - K = C - v k - K Now the second member being a function of an arbitrary constant is equivalent to an arbitrary constant and may be replaced by ...
Page 12
... assumed that a solution for dy which = 0 is always to count as a singular solution , even if de it should coincide with a particular integral . This does not seem to have been quite the view of the former part of Chap- ter VIII . see ...
... assumed that a solution for dy which = 0 is always to count as a singular solution , even if de it should coincide with a particular integral . This does not seem to have been quite the view of the former part of Chap- ter VIII . see ...
Page 16
... to the same limitations 2ndly . It may be that dp dy dx d or assumes for a particu- In this • lar relation between x and y the indefinite form . case we must seek by the development of its terms 16 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
... to the same limitations 2ndly . It may be that dp dy dx d or assumes for a particu- In this • lar relation between x and y the indefinite form . case we must seek by the development of its terms 16 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
Page 24
... assume the form du dx = f ( x , ủ ) . Now this equation being satisfied by u = 0 and the first member vanishing , the second must also . Poisson now assumes , and the assumption must be carefully noted , this second member to be capable ...
... assume the form du dx = f ( x , ủ ) . Now this equation being satisfied by u = 0 and the first member vanishing , the second must also . Poisson now assumes , and the assumption must be carefully noted , this second member to be capable ...
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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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