A Treatise on Differential Equations. Supplementary VolumeMacmillan, 1865 - 235 σελίδες |
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Σελίδα 23
... us represent the given singular solution of the dif ferential equation by u = u being a given function of x and y . Then introducing u and x instead of y and x as variables , the ART . 8. ] 23 ADDITIONS TO CHAPTER VIII .
... us represent the given singular solution of the dif ferential equation by u = u being a given function of x and y . Then introducing u and x instead of y and x as variables , the ART . 8. ] 23 ADDITIONS TO CHAPTER VIII .
Σελίδα 68
... introducing a new system of independent variables . The actual transformation is greatly facilitated by the following symbolical theorem . THEOREM . If the partial differential equation dz dz X , dx , + X 2 dx z ... + X dz = X be ...
... introducing a new system of independent variables . The actual transformation is greatly facilitated by the following symbolical theorem . THEOREM . If the partial differential equation dz dz X , dx , + X 2 dx z ... + X dz = X be ...
Σελίδα 84
... introducing u ,, u ,, ..... Um - 1 , x , as independent variables . Those equations being AP = 0 , ...... A „ P = 0 , the result of the transformation will be ( Chap . XXIV . Art . 7 ) dP ( A ̧21 ) du + ( A ̧2 ) du , dP dP dP ...... + ...
... introducing u ,, u ,, ..... Um - 1 , x , as independent variables . Those equations being AP = 0 , ...... A „ P = 0 , the result of the transformation will be ( Chap . XXIV . Art . 7 ) dP ( A ̧21 ) du + ( A ̧2 ) du , dP dP dP ...... + ...
Σελίδα 164
... formula dz = pdx + qdy , inte- grating , replacing the arbitrary form ff , ( 1 ) dt by ( m , − m . ) $ ( 1 ) , - and introducing an arbitrary function of C for the arbitrary 164 PARTIAL DIFFERENTIAL EQUATIONS [ CH . XXIX .
... formula dz = pdx + qdy , inte- grating , replacing the arbitrary form ff , ( 1 ) dt by ( m , − m . ) $ ( 1 ) , - and introducing an arbitrary function of C for the arbitrary 164 PARTIAL DIFFERENTIAL EQUATIONS [ CH . XXIX .
Σελίδα 165
George Boole Isaac Todhunter. and introducing an arbitrary function of C for the arbitrary constant , we have 2 = [ 2 ay2 -・ m1xy + - 2 + Cx + $ { ( m2 − m12 ) y + C } | + † ( C ) m ̧ ) for a complete primitive . The general primitive ...
George Boole Isaac Todhunter. and introducing an arbitrary function of C for the arbitrary constant , we have 2 = [ 2 ay2 -・ m1xy + - 2 + Cx + $ { ( m2 − m12 ) y + C } | + † ( C ) m ̧ ) for a complete primitive . The general primitive ...
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Algebra arbitrary constants Calculus of Variations Cambridge Chap Chapter Christ's College cloth College complete primitive condition Conic Sections contains Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dF dp dp dx dp dq dp dy dq dp du₂ dx dx dx dy dx₁ dx² dy dp dy dx dy dy dy dz dz dy dz dz eliminate English equa expression Extra fcap factor fcap function Geometry given equation Grammar Hence homogeneous function Last Multiplier Latin linear partial differential m₁ Mathematical method ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole proposition reduced relation represent result Schools Second Edition singular solution theorem theory tion transformation Trigonometry u₁ values vanish x₁ Y₁ аф
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