A Treatise on Differential Equations, Τόμος 2Macmillan and Company, 1865 |
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Σελίδα 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 ...
Σελίδα 64
... combination with the equation dF du , dF du dF du + ... + du , dz du , dz du dz dF = 0 , dz we can eliminate dF dF dF dF du , ' du ' du ' dz The result will be du , dua dun dx1 ' dx dx1 Pi du , du Jun dx dx dx Pn du , du dun dz - " -1 ...
... combination with the equation dF du , dF du dF du + ... + du , dz du , dz du dz dF = 0 , dz we can eliminate dF dF dF dF du , ' du ' du ' dz The result will be du , dua dun dx1 ' dx dx1 Pi du , du Jun dx dx dx Pn du , du dun dz - " -1 ...
Σελίδα 65
... combination du1 du1 + X2 Xs dx s -2 dx2 du 2 dur + X 2 dxx 2 X1 Jx 、 B. D. E. II . dic ... ... with the corresponding equations , + R du1 = 0 , du + Xn dx dun + X + R dxn dz dun dz = 0 , 5 eliminating X , X2 , ... X , R we ART . 3 ...
... combination du1 du1 + X2 Xs dx s -2 dx2 du 2 dur + X 2 dxx 2 X1 Jx 、 B. D. E. II . dic ... ... with the corresponding equations , + R du1 = 0 , du + Xn dx dun + X + R dxn dz dun dz = 0 , 5 eliminating X , X2 , ... X , R we ART . 3 ...
Σελίδα 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 ...
Σελίδα 88
... other equations are derivable from these . We conclude that there is but one final integral . To obtain it , eliminate dP dP dx ' dy " dP dt from the above system combined with dP dP dx + 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 dx ' dy " dP dt from the above system combined with dP dP dx + 88 [ CH . XXV . LINEAR PARTIAL DIFFERENTIAL.
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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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