A Treatise on Differential Equations, Τόμος 2Macmillan and Company, 1865 |
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Σελίδα 17
... known modes its true limiting value or values . Finite values will indicate particular primitives , infinite values sin- gular solutions , and when such values emerge together out of the same relation between the variables , the ...
... known modes its true limiting value or values . Finite values will indicate particular primitives , infinite values sin- gular solutions , and when such values emerge together out of the same relation between the variables , the ...
Σελίδα 23
... known . His demonstration is in substance as follows . Let us represent the given singular solution of the dif ferential equation by u = 0 , u being a given function of x and y . Then introducing u and x instead of y and x as variables ...
... known . His demonstration is in substance as follows . Let us represent the given singular solution of the dif ferential equation by u = 0 , u being a given function of x and y . Then introducing u and x instead of y and x as variables ...
Σελίδα 26
... known by integration when that of U is given . And again , transform the differential equation by making v and x the variables instead of u and x . We have dv dx ( doc ) dx dv dv du = + dx du dx • in which is the differential ...
... known by integration when that of U is given . And again , transform the differential equation by making v and x the variables instead of u and x . We have dv dx ( doc ) dx dv dv du = + dx du dx • in which is the differential ...
Σελίδα 38
... known . The reduction may however be effected immediately by the method of the variation of parameters . In this and in most general investigations connected with differential equa- tions great advantages in point of brevity and of the ...
... known . The reduction may however be effected immediately by the method of the variation of parameters . In this and in most general investigations connected with differential equa- tions great advantages in point of brevity and of the ...
Σελίδα 40
... known functions of x . known quantities de Thus the r un- dc , are made to depend upon only " ... dx dx one unknown quantity , viz . z . It remains then to deter- mine z . For this purpose we must complete the expression of the ...
... known functions of x . known quantities de Thus the r un- dc , are made to depend upon only " ... dx dx one unknown quantity , viz . z . It remains then to deter- mine z . For this purpose we must complete the expression of the ...
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arbitrary constants C₂ Chap Chapter cloth common integral complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dp dx dp dq dp dy dp₁ dq dp du₁ dx dp dx dx dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz eliminate equa expression Extra fcap factor Fcap given equation Heir of Redclyffe Hence HENRY KINGSLEY homogeneous function independent variables infinite Jacobi JAMES MCCOSH Last Multiplier linear partial differential m₁ memoir obtain ordinary differential equations P₁ partial differential equation particular integral Professor Boole proposition reduced represent result Second Edition shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence x₁ Y₁ аф
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