A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página viii
... Combination of Testimonies or Judgments . Vol . 21 , 1857 , pages 597 ... 653 . In the Bulletin de l'Académie ... de St Pétersbourg . Considérations sur la recherche des intégrales premières des équations différentielles partielles du ...
... Combination of Testimonies or Judgments . Vol . 21 , 1857 , pages 597 ... 653 . In the Bulletin de l'Académie ... de St Pétersbourg . Considérations sur la recherche des intégrales premières des équations différentielles partielles du ...
Página 64
... combination with the equation dF du ,, dF du2 dF du + dF dz = 0 , ... + - dun dz we can eliminate dF dF du , ' du dF dF dun ' dz The result will be du , du dun dx dx dxx Pi du , du du = = 0 , dx dx ' dx 9 Pr du , du dun dz dz ว dz ' -1 ...
... combination with the equation dF du ,, dF du2 dF du + dF dz = 0 , ... + - dun dz we can eliminate dF dF du , ' du dF dF dun ' dz The result will be du , du dun dx dx dxx Pi du , du du = = 0 , dx dx ' dx 9 Pr du , du dun dz dz ว dz ' -1 ...
Página 65
... combination X1 dx s dux du z 2 dun dun + X2 dic2 Xs Jor dx dx1 B. D. E. II . dz - 0 , with the corresponding equations , du du , + R ... + Xn dxn dun + Xn + R dxn ... dz dun dz = = 0 , = 0 , 5 ... eliminating X , X2 , ... X , R ART . 3 ...
... combination X1 dx s dux du z 2 dun dun + X2 dic2 Xs Jor dx dx1 B. D. E. II . dz - 0 , with the corresponding equations , du du , + R ... + Xn dxn dun + Xn + R dxn ... dz dun dz = = 0 , = 0 , 5 ... eliminating X , X2 , ... X , R ART . 3 ...
Página 87
... combined together so as to form an equal number of equivalent equations of the exact form . Generally when we know this combination to be possible it is easy to effect it , and best to endeavour to do so . We might how- ever employ the ...
... combined together so as to form an equal number of equivalent equations of the exact form . Generally when we know this combination to be possible it is easy to effect it , and best to endeavour to do so . We might how- ever employ the ...
Página 88
... other equations are derivable from these . We conclude that there is but one final integral . To obtain it , eliminate dP dP dP dx ' dy ' dt from the above system combined with dP dP dP dP 88 [ CH . XXV . LINEAR PARTIAL DIFFERENTIAL.
... other equations are derivable from these . We conclude that there is but one final integral . To obtain it , eliminate dP dP dP dx ' dy ' dt from the above system combined with dP dP dP dP 88 [ CH . XXV . LINEAR PARTIAL DIFFERENTIAL.
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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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