A Treatise on Differential Equations, Τόμος 2Macmillan and Company, 1865 |
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Σελίδα 5
... connecting x and y may be shewn thus . Let y = ( x 。, Yo , x ) be the relation between x and y indicated by the supposed motion , x , y , being the initial point of departure . Then this point being on the line of motion , x , y , are ...
... connecting x and y may be shewn thus . Let y = ( x 。, Yo , x ) be the relation between x and y indicated by the supposed motion , x , y , being the initial point of departure . Then this point being on the line of motion , x , y , are ...
Σελίδα 32
... connecting properties of different branches of the same curve . Taylor gave them the name singular , while Clairaut , and Euler too in his memoir , regarded them as a species of paradox , not merely from their non - inclusion in the ...
... connecting properties of different branches of the same curve . Taylor gave them the name singular , while Clairaut , and Euler too in his memoir , regarded them as a species of paradox , not merely from their non - inclusion in the ...
Σελίδα 94
... connecting the above variables with the constants c , C2 , ..... C - 1 . Finally , solving these equations with respect to the constants , we shall possess the integrals required in the form F1 ( † , d ' ‚ ......... .. qu − 1 ) ) = C1 ...
... connecting the above variables with the constants c , C2 , ..... C - 1 . Finally , solving these equations with respect to the constants , we shall possess the integrals required in the form F1 ( † , d ' ‚ ......... .. qu − 1 ) ) = C1 ...
Σελίδα 105
... connecting the new functions F ,, ..... F with F , be identi- cally satisfied , but also the series of conditions [ FF ] = 0 ...... ...... ( 4 ) , F and F representing any two of the new functions re- ferred to . The first of the above ...
... connecting the new functions F ,, ..... F with F , be identi- cally satisfied , but also the series of conditions [ FF ] = 0 ...... ...... ( 4 ) , F and F representing any two of the new functions re- ferred to . The first of the above ...
Σελίδα 113
... connecting x ,, ... n , z , P1 , ... Pa , from which with the aid of the given equation p ,, ... Pa may be eliminated , and there will result a single equation connecting xn with z . This is the integral sought . " ... [ It appears from ...
... connecting x ,, ... n , z , P1 , ... Pa , from which with the aid of the given equation p ,, ... Pa may be eliminated , and there will result a single equation connecting xn with z . This is the integral sought . " ... [ It appears from ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
arbitrary constants C₂ Chap Chapter cloth common integral complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dp dx dp dq dp dy dp₁ dq dp du₁ dx dp dx dx dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz eliminate equa expression Extra fcap factor Fcap given equation Heir of Redclyffe Hence HENRY KINGSLEY homogeneous function independent variables infinite Jacobi JAMES MCCOSH Last Multiplier linear partial differential m₁ memoir obtain ordinary differential equations P₁ partial differential equation particular integral Professor Boole proposition reduced represent result Second Edition shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence x₁ Y₁ аф
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