A Treatise on Differential Equations |
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Page 1
... dx ' + ( A'x ' + C ' ) dy ' = 0 ............... . ( 1 ) x ' = x + m2y , y ' = = x + m2y • It will be seen that in these equations united we have as many constants as in the original equation . Now on substi- tuting in the assumed ...
... dx ' + ( A'x ' + C ' ) dy ' = 0 ............... . ( 1 ) x ' = x + m2y , y ' = = x + m2y • It will be seen that in these equations united we have as many constants as in the original equation . Now on substi- tuting in the assumed ...
Page 5
... dy dx = f ( x , y ) , we see that the direction of motion is constantly assigned as a function of the co - ordinates of position . The entire motion is therefore determinate as soon as the initial point is fixed . The result of the ...
... dy dx = f ( x , y ) , we see that the direction of motion is constantly assigned as a function of the co - ordinates of position . The entire motion is therefore determinate as soon as the initial point is fixed . The result of the ...
Page 6
... dx 。 + f1 ( x 。, Yo ) = 0 , dy 。 whence in particular dA . dA . + f1 ( xo , Yo ) dyo = = 0 . Eliminate between these equations f ( x , y ) , and we have dA , dA dA , dA - dx dy dy dx . = 0 . Therefore , by Prop . I. , A , is a ...
... dx 。 + f1 ( x 。, Yo ) = 0 , dy 。 whence in particular dA . dA . + f1 ( xo , Yo ) dyo = = 0 . Eliminate between these equations f ( x , y ) , and we have dA , dA dA , dA - dx dy dy dx . = 0 . Therefore , by Prop . I. , A , is a ...
Page 10
... dx dy_df ( x , c ) , df ( x , c ) dc dx dx + dc dx can be equivalent when c is variable , are ( 1 ) when df ( x , c ) dc = = 0 , ( 2 ) when df ( x , c ) = ∞ ; dx dy dx in the latter case = : 00 , and therefore = 0 , and this dx dy ...
... dx dy_df ( x , c ) , df ( x , c ) dc dx dx + dc dx can be equivalent when c is variable , are ( 1 ) when df ( x , c ) dc = = 0 , ( 2 ) when df ( x , c ) = ∞ ; dx dy dx in the latter case = : 00 , and therefore = 0 , and this dx dy ...
Page 11
... dy = ∞ Professor Boole met the objection in substance thus : " It will be ... 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 ...
... dy = ∞ Professor Boole met the objection in substance thus : " It will be ... 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 ...
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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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