A Treatise on Differential Equations |
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Page 2
... represented by u = C , C being the arbitrary constant and u a function of x , y , and constants which are not arbitrary . Suppose too that when one of these constants k assumes a particular value ê , the function u reduces to a constant ...
... represented by u = C , C being the arbitrary constant and u a function of x , y , and constants which are not arbitrary . Suppose too that when one of these constants k assumes a particular value ê , the function u reduces to a constant ...
Page 3
... Representing these func- tions by ( m ) , ( m , ) respectively , we have u = $ ( m , ) ф ( та ) But m ,, m , being roots of a quadratic equation may be represented in the form m1 = m + k , m2 = mk , the roots becoming equal when l = 0 ...
... Representing these func- tions by ( m ) , ( m , ) respectively , we have u = $ ( m , ) ф ( та ) But m ,, m , being roots of a quadratic equation may be represented in the form m1 = m + k , m2 = mk , the roots becoming equal when l = 0 ...
Page 4
... equation of finite differences ( Eq . ( 3 ) , Chap . 11. ) . But if we represent x and y by the rectangular co - ordinates of a moving point on a plane the differential equation 4 [ CH . XIX . ADDITIONS TO CHAPTER II .
... equation of finite differences ( Eq . ( 3 ) , Chap . 11. ) . But if we represent x and y by the rectangular co - ordinates of a moving point on a plane the differential equation 4 [ CH . XIX . ADDITIONS TO CHAPTER II .
Page 6
... represented by Хо y — y 。= f ( x 。, y . ) ( x − x . ) . On these principles Cauchy has founded remarkable methods of solution , which deserve attention from the commentary on the limits of error on their application by which they are ...
... represented by Хо y — y 。= f ( x 。, y . ) ( x − x . ) . On these principles Cauchy has founded remarkable methods of solution , which deserve attention from the commentary on the limits of error on their application by which they are ...
Page 7
... represent a curve consisting of two branches , and giving to every possible value we obtain an infinite system of such curves , each consisting of two branches . The aggregate of branches thus obtained is evidently the same as the aggre ...
... represent a curve consisting of two branches , and giving to every possible value we obtain an infinite system of such curves , each consisting of two branches . The aggregate of branches thus obtained is evidently the same as the aggre ...
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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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