A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 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 ...
Página 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 ...
Página 94
... connecting the above variables with the constants c1 , C , ..... Cu - 1 . Finally , solving these equations with respect to the constants , we shall possess the integrals required in the form == F ( p , ' , ..... -1 ) ) = C1 ...
... connecting the above variables with the constants c1 , C , ..... Cu - 1 . Finally , solving these equations with respect to the constants , we shall possess the integrals required in the form == F ( p , ' , ..... -1 ) ) = C1 ...
Página 105
... connecting the new functions F ,, ..... F with F , be identi- cally satisfied , but also the series of conditions [ F.F . ] = 0 .... ....... ( 4 ) , F and F representing any two of the new functions re- ferred to . The first of the ...
... connecting the new functions F ,, ..... F with F , be identi- cally satisfied , but also the series of conditions [ F.F . ] = 0 .... ....... ( 4 ) , F and F representing any two of the new functions re- ferred to . The first of the ...
Página 113
... connecting 1 , ... xn , Z , P1 , ... Pn , from which with the aid of the given equation P1 , ... P may be eliminated , and there will result a single equation connecting xn with z . This is the integral sought . X11 ... [ It appears ...
... connecting 1 , ... xn , Z , P1 , ... Pn , from which with the aid of the given equation P1 , ... P may be eliminated , and there will result a single equation connecting xn with z . This is the integral sought . X11 ... [ It appears ...
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Términos y frases comunes
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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