A Treatise on Differential Equations |
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Page 10
... dx dy_df ( x , c ) , df ( x , c ) dc dx dx + dc dx can be equivalent when c ... dp dy = ∞ that it leads to solutions involving y at least . " It is ob ... dp p = x " y ; here if n is negative , dy is infinite when x = 0 , and xn + 1 this ...
... dx dy_df ( x , c ) , df ( x , c ) dc dx dx + dc dx can be equivalent when c ... dp dy = ∞ that it leads to solutions involving y at least . " It is ob ... dp p = x " y ; here if n is negative , dy is infinite when x = 0 , and xn + 1 this ...
Page 11
... dp dy = ∞ Professor Boole met the objection in substance thus : " It will ... dx - Hence x = 0 , provided n is between 0 and 1 , or y = 0 . Consider these ... dx = ∞ we have no inference ; from the fact that it does not come from dp d ...
... dp dy = ∞ Professor Boole met the objection in substance thus : " It will ... dx - Hence x = 0 , provided n is between 0 and 1 , or y = 0 . Consider these ... dx = ∞ we have no inference ; from the fact that it does not come from dp d ...
Page 12
... dx - - 1 ( ) = ∞ , we infer that it is a particular integral . To prove this we have c = ye xn + 1 n + 1 . When 0 ... dp dy = leads to a solution which does not involve y nothing is to be inferred ... is important . It corrects the state- ...
... dx - - 1 ( ) = ∞ , we infer that it is a particular integral . To prove this we have c = ye xn + 1 n + 1 . When 0 ... dp dy = leads to a solution which does not involve y nothing is to be inferred ... is important . It corrects the state- ...
Page 14
... dx dc = = 0 . 5. We have seen that the equation dy = 0 may be satisfied dc by an absolutely constant value of c , so ... dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH ...
... dx dc = = 0 . 5. We have seen that the equation dy = 0 may be satisfied dc by an absolutely constant value of c , so ... dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH ...
Page 15
... dp = 0 , = ∞ dy There is another not less important . As the numerator of ( 9 ) may become infinite not only when ... dx dc Exactly in the same way the condition = 0 , as relating to the complete primitive , leads to the condition . d dx ...
... dp = 0 , = ∞ dy There is another not less important . As the numerator of ( 9 ) may become infinite not only when ... dx dc Exactly in the same way the condition = 0 , as relating to the complete primitive , leads to the condition . d dx ...
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Common terms and phrases
arbitrary constants Cambridge Chap Chapter College complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dF dF dp dF dx dFdF differential coefficients dp dF dp dp dx dp dq dp dy dp₁ dq dp dv dv dx dp dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor function given equation Hence J. P. MAHAFFY Jacobi Last Multiplier linear partial differential m₁ memoir ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole reduced represent result revised School shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence X₁ Y₁ аф
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