A Treatise on Differential Equations. Supplementary Volume |
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Page 9
... important in his work . He continued his re- searches after the publication of his first edition , and intended to reconstruct the Chapter with great improvements in the second edition . After carefully examining the manuscripts I came ...
... important in his work . He continued his re- searches after the publication of his first edition , and intended to reconstruct the Chapter with great improvements in the second edition . After carefully examining the manuscripts I came ...
Page 12
... important . It corrects the state- ment put too strongly in Chap . VIII . Art . 7 , “ All we can affirm is that if dp = gives a solution at all it will be a singular solution . " dy From Art . 8 onwards it seems assumed that a solution ...
... important . It corrects the state- ment put too strongly in Chap . VIII . Art . 7 , “ All we can affirm is that if dp = gives a solution at all it will be a singular solution . " dy From Art . 8 onwards it seems assumed that a solution ...
Page 13
... important remark yet remains . The elimination of c between a primitive y = f ( x , c ) and the derived equation dy = 0 , does not necessarily lead to a singular solution in the dc sense above explained . For it is possible that the ART ...
... important remark yet remains . The elimination of c between a primitive y = f ( x , c ) and the derived equation dy = 0 , does not necessarily lead to a singular solution in the dc sense above explained . For it is possible that the ART ...
Page 15
... important . As the numerator of ( 9 ) may become infinite not only when ( x , c ) = 0 , but also when ( x , c ) = infinite , we see that a relation between y and a which makes infinite will not necessarily satisfy dp dy the differential ...
... important . As the numerator of ( 9 ) may become infinite not only when ( x , c ) = 0 , but also when ( x , c ) = infinite , we see that a relation between y and a which makes infinite will not necessarily satisfy dp dy the differential ...
Page 16
... important results of the foregoing investigations in the following theorem . THEOREM . Every solution of a differential equation of the first order which is derived from the complete primitive by giving to c a variable value will , if ...
... important results of the foregoing investigations in the following theorem . THEOREM . Every solution of a differential equation of the first order which is derived from the complete primitive by giving to c a variable value will , if ...
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Common terms and phrases
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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