A Treatise on Differential Equations |
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Page 71
... dp dx dq dy dz and the conditions dF dp = 0 , dF dq = 0 , necessary to reduce the equation for dz to a lower order give ( px - qy ) q − 2mx3 = 0 , - ( px - qy ) ( px - 3qy ) = 0 . From these we find p = 3m * x * y * , q = m * x * y ...
... dp dx dq dy dz and the conditions dF dp = 0 , dF dq = 0 , necessary to reduce the equation for dz to a lower order give ( px - qy ) q − 2mx3 = 0 , - ( px - qy ) ( px - 3qy ) = 0 . From these we find p = 3m * x * y * , q = m * x * y ...
Page 121
... dp dq + dF / dv dv dv \ dx + dzP + du du du dp s + dF / dv dv dv + 2+ dv dy dz dp dv dp dv dq r + S = 0 , dq 1 ) s + dq dv t = 0 . t For brevity , write du du du du du du for and dx + P Jz ' for dy dy ' +9 dz ' and then eliminating dF ...
... dp dq + dF / dv dv dv \ dx + dzP + du du du dp s + dF / dv dv dv + 2+ dv dy dz dp dv dp dv dq r + S = 0 , dq 1 ) s + dq dv t = 0 . t For brevity , write du du du du du du for and dx + P Jz ' for dy dy ' +9 dz ' and then eliminating dF ...
Page 122
... dp dq = du du + s + dp dq dv + dps + dv ) du dv th , 1 } { ( do ) + dv dp which , on effecting the multiplication , gives ( du ( dv dp dy ( du dv dy dp ( ) ( ) + + r dv du dv - dv dv r + dq " dp ( dx ) - ( dy ) do + du ( du ) ...
... dp dq = du du + s + dp dq dv + dps + dv ) du dv th , 1 } { ( do ) + dv dp which , on effecting the multiplication , gives ( du ( dv dp dy ( du dv dy dp ( ) ( ) + + r dv du dv - dv dv r + dq " dp ( dx ) - ( dy ) do + du ( du ) ...
Page 125
... dq dy dp + U dx dFdF dy dF dF + V 0 , dp dq R dq 2 - dF dF S + T dq .ART . 4. ] 125 OF THE SECOND ORDER .
... dq dy dp + U dx dFdF dy dF dF + V 0 , dp dq R dq 2 - dF dF S + T dq .ART . 4. ] 125 OF THE SECOND ORDER .
Page 126
George Boole. R dq 2 - dF dF S + T dq dp + U 2 in which dF dx dFdF { ( da ) dp dx dF dF dF = dx + P dz ' dy ( 2/4 ) = dF dy + dFdF dy 21 } = 0 ; dF + q dz dq Regarding the function F in the proposed integral F = 0 simply as a function ...
George Boole. R dq 2 - dF dF S + T dq dp + U 2 in which dF dx dFdF { ( da ) dp dx dF dF dF = dx + P dz ' dy ( 2/4 ) = dF dy + dFdF dy 21 } = 0 ; dF + q dz dq Regarding the function F in the proposed integral F = 0 simply as a function ...
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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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