A Treatise on Differential Equations |
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Page xii
... PARTIAL DIFFER- ENTIAL EQUATIONS OF THE FIRST ORDER , AND ON Asso- CIATED SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS XXVI . HOMOGENEOUS SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS • PAGH Ι 7 • 9 38 46 56 74 · • 90 XXVII . OF NON ...
... PARTIAL DIFFER- ENTIAL EQUATIONS OF THE FIRST ORDER , AND ON Asso- CIATED SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS XXVI . HOMOGENEOUS SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS • PAGH Ι 7 • 9 38 46 56 74 · • 90 XXVII . OF NON ...
Page 59
... ] 2. As it has been shewn that a primitive u = ( v ) leads to a linear partial differential equation of the form Pp Qq = R .... ...... ( 1 ) . ( 2 ) , provided that u = a , v = b , ART . 2. ] 59 ADDITIONS TO CHAPTER XIV .
... ] 2. As it has been shewn that a primitive u = ( v ) leads to a linear partial differential equation of the form Pp Qq = R .... ...... ( 1 ) . ( 2 ) , provided that u = a , v = b , ART . 2. ] 59 ADDITIONS TO CHAPTER XIV .
Page 60
... differential equations dx dy dz = = P Q R ( 3 ) , it is evident that we shall obtain a solution of the partial dif- ferential equation ( 2 ) by constructing the system of ordinary differential equations ( 3 ) , deducing their general ...
... differential equations dx dy dz = = P Q R ( 3 ) , it is evident that we shall obtain a solution of the partial dif- ferential equation ( 2 ) by constructing the system of ordinary differential equations ( 3 ) , deducing their general ...
Page 61
... differential equations dx_dy_dz = = P Q R deduce their general integrals in ... equations of the first order , without regard to the number of the ... partial differential equation obtained by eliminating dz , dx ,, dx , ... dx ...
... differential equations dx_dy_dz = = P Q R deduce their general integrals in ... equations of the first order , without regard to the number of the ... partial differential equation obtained by eliminating dz , dx ,, dx , ... dx ...
Page 63
... equation - p1dx1 + p2dx2 ... + p2dx „ — dz = 0 , and eliminating the differentials , we find X11 + X2 P2 + XnPn = R for the partial differential equation sought . 2nd proof . Differentiating the given primitive with respect tox , as ...
... equation - p1dx1 + p2dx2 ... + p2dx „ — dz = 0 , and eliminating the differentials , we find X11 + X2 P2 + XnPn = R for the partial differential equation sought . 2nd proof . Differentiating the given primitive with respect tox , as ...
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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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