A Treatise on Differential Equations. Supplementary Volume |
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Page 10
... df ( x , c ) de and = dx dx can be equivalent when c is variable , are + dc ... dp In Art . 8 of Chapter VIII . we read , " We may pass over the case in ... dp x = dy is infinite when x = 0 , and dy xn + 1 this is a singular solution ...
... df ( x , c ) de and = dx dx can be equivalent when c is variable , are + dc ... dp In Art . 8 of Chapter VIII . we read , " We may pass over the case in ... dp x = dy is infinite when x = 0 , and dy xn + 1 this is a singular solution ...
Page 14
... df ( x , c ) dc = 0 may neither on the one hand enable us to determine c as a function of x , so leading to a ... dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH . XXI ...
... df ( x , c ) dc = 0 may neither on the one hand enable us to determine c as a function of x , so leading to a ... dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH . XXI ...
Page 71
... dF dôz dF + Sz = 0 , dp dx dq dy dz and the conditions dF dp = 0 , dF dq = 0 , necessary to reduce the equation for dz to a lower order give ( px - qy ) q − 2mx3 = 0 , - ( px — qy ) ( px - 3qy ) = 0 . From these we find - p = 3m1x * y ...
... dF dôz dF + Sz = 0 , dp dx dq dy dz and the conditions dF dp = 0 , dF dq = 0 , necessary to reduce the equation for dz to a lower order give ( px - qy ) q − 2mx3 = 0 , - ( px — qy ) ( px - 3qy ) = 0 . From these we find - p = 3m1x * y ...
Page 93
George Boole Isaac Todhunter. dF φ ' аф dF + $ " + do ' ...... + фш - 1 ) dF døm - 2 ) + ƒ ( P , $ ' , ( -1 ) ... dp * in terms of the variables p , p , ...- 1 ) . Proceeding with this in the same way and continuing the process we shall be able ...
George Boole Isaac Todhunter. dF φ ' аф dF + $ " + do ' ...... + фш - 1 ) dF døm - 2 ) + ƒ ( P , $ ' , ( -1 ) ... dp * in terms of the variables p , p , ...- 1 ) . Proceeding with this in the same way and continuing the process we shall be able ...
Page 98
... dF do dFdọ + Pi dz dp , dpdx . dp + Pi dz 0 , the summation extending to all values of i , from 1 to n inclusive , will be satisfied identically . Reciprocally , if the above condition be satisfied identically for 98 [ CH , XXVII . NON ...
... dF do dFdọ + Pi dz dp , dpdx . dp + Pi dz 0 , the summation extending to all values of i , from 1 to n inclusive , will be satisfied identically . Reciprocally , if the above condition be satisfied identically for 98 [ CH , XXVII . NON ...
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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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