A Treatise on Differential Equations. Supplementary Volume |
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Page 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 ...
Page 23
... known . His demonstration is in substance as follows . Let 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 ...
... known . His demonstration is in substance as follows . Let 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 ...
Page 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 ' dv dv dv du ( doc ) dx = + 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 ' dv dv dv du ( doc ) dx = + dx du dx in which is the differential ...
Page 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 ...
Page 40
... known functions of x . Thus the run- 19 known quantities dc1 dcr " ... dx dx are made to depend upon only 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 . Thus the run- 19 known quantities dc1 dcr " ... dx dx are made to depend upon only 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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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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