A Treatise on Differential Equations |
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Page ix
... Transformations . Vol . 3 , 1843 , pages 1 ... 20 , 106 ... 119 . On the Transformation of Definite Integrals . pages 216 ... 224 . Same Vol . , Remarks on a Theorem of M. Catalan . Same Vol . , pages 277 ... 283 . On the Transformation ...
... Transformations . Vol . 3 , 1843 , pages 1 ... 20 , 106 ... 119 . On the Transformation of Definite Integrals . pages 216 ... 224 . Same Vol . , Remarks on a Theorem of M. Catalan . Same Vol . , pages 277 ... 283 . On the Transformation ...
Page 1
... transformation by which the equa- tion may be reduced to , ( because it may be constructed from ) , an equation in which the variables are separated . Assume as this equation and let ( Ay ' + C ' ) dx ' + ( A'x ' + C ' ) dy ' = 0 ...
... transformation by which the equa- tion may be reduced to , ( because it may be constructed from ) , an equation in which the variables are separated . Assume as this equation and let ( Ay ' + C ' ) dx ' + ( A'x ' + C ' ) dy ' = 0 ...
Page 24
... transformation will assume the form du = f ( x , u ) . dx Now this equation being satisfied by u = 0 and the first member vanishing , the second must also . Poisson now assumes , and the assumption must be carefully noted , this second ...
... transformation will assume the form du = f ( x , u ) . dx Now this equation being satisfied by u = 0 and the first member vanishing , the second must also . Poisson now assumes , and the assumption must be carefully noted , this second ...
Page 25
... transformation , but through the rejection of an algebraic factor u from the transformed equation . It has been shewn in the treatment of Clairaut's equation , how in the ascent by differentiation to an equation of a higher order a ...
... transformation , but through the rejection of an algebraic factor u from the transformed equation . It has been shewn in the treatment of Clairaut's equation , how in the ascent by differentiation to an equation of a higher order a ...
Page 26
... transformation which introduces u and x as variables becomes Let du = dx QU . du 0 v = v , so that is in general a function of x and u , the form of which is known by integration when that of U is given . And again , transform the ...
... transformation which introduces u and x as variables becomes Let du = dx QU . du 0 v = v , so that is in general a function of x and u , the form of which is known by integration when that of U is given . And again , transform the ...
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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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