A Treatise on Differential Equations. Supplementary VolumeMacmillan, 1865 - 235 pages |
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Page 10
... df ( x , c ) de and = dx dx can be equivalent when c is variable , are + dc ... dp In Art . 8 of Chapter VIII . we read , " We may pass over the case in ... dp x = dy is infinite when x = 0 , and dy xn + 1 this is a singular solution ...
... df ( x , c ) de and = dx dx can be equivalent when c is variable , are + dc ... dp In Art . 8 of Chapter VIII . we read , " We may pass over the case in ... dp x = dy is infinite when x = 0 , and dy xn + 1 this is a singular solution ...
Page 14
... df ( x , c ) dc = 0 may neither on the one hand enable us to determine c as a function of x , so leading to a ... dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH . XXI ...
... df ( x , c ) dc = 0 may neither on the one hand enable us to determine c as a function of x , so leading to a ... dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH . XXI ...
Page 16
... of the condition dy dc = 0 to the complete primitive . The distinction of character of the two tests is here made ... dp = ∞ ; dy and if it involve x , the relation d ( 1 dx = ∞ But relations satisfying these conditions will not ...
... of the condition dy dc = 0 to the complete primitive . The distinction of character of the two tests is here made ... dp = ∞ ; dy and if it involve x , the relation d ( 1 dx = ∞ But relations satisfying these conditions will not ...
Page 20
... of dy day , & c . ad inf . , as derived from the dx ' dx2 ' differential equation , are the same as those derived from the complete primitive . But a solution deduced from the condition constructed so as to yield the same value of dp ...
... of dy day , & c . ad inf . , as derived from the dx ' dx2 ' differential equation , are the same as those derived from the complete primitive . But a solution deduced from the condition constructed so as to yield the same value of dp ...
Page 71
George Boole Isaac Todhunter. Representing the first member of the equation by F , we` have , on operating by 8 , dF d8z + dF dôz dF + Sz = 0 , dp dx dq dy dz and the conditions dF dp = 0 , dF dq = 0 , necessary to reduce the equation ...
George Boole Isaac Todhunter. Representing the first member of the equation by F , we` have , on operating by 8 , dF d8z + dF dôz dF + Sz = 0 , dp dx dq dy dz and the conditions dF dp = 0 , dF dq = 0 , necessary to reduce the equation ...
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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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