A Treatise on Differential Equations. Supplementary VolumeMacmillan, 1865 - 235 σελίδες |
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Σελίδα 3
... becomes ( du dk = = C. = In applying this theory to the reduction of the general solution ( 2 ) in the case in which m m2 , it must be observed that the numerator of the first member is the same function of m ,, x , y , as the ...
... becomes ( du dk = = C. = In applying this theory to the reduction of the general solution ( 2 ) in the case in which m m2 , it must be observed that the numerator of the first member is the same function of m ,, x , y , as the ...
Σελίδα 4
... becomes on putting C for d dm log 4 ( m ) = C , d 1 or dm am -a - log { ( am — a ' ) ( x + my ) + cm − c ' } = C. 3. [ The next Article seems to have been intended to ap- pear in the enlarged form of Chap . II .; but I cannot discover ...
... becomes on putting C for d dm log 4 ( m ) = C , d 1 or dm am -a - log { ( am — a ' ) ( x + my ) + cm − c ' } = C. 3. [ The next Article seems to have been intended to ap- pear in the enlarged form of Chap . II .; but I cannot discover ...
Σελίδα 14
... It would not there- fore be infinite . Hence we conclude that would not become dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
... It would not there- fore be infinite . Hence we conclude that would not become dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
Σελίδα 15
... become infinite not only when ( x , c ) = 0 , but also when ( x , c ) = infinite , we see that a relation between y and ... becomes infinite when y = 0. As this involves y and satisfies the differential equation it is a singular solution ...
... become infinite not only when ( x , c ) = 0 , but also when ( x , c ) = infinite , we see that a relation between y and ... becomes infinite when y = 0. As this involves y and satisfies the differential equation it is a singular solution ...
Σελίδα 17
... becomes infinite if x = 0 ; but this not involving y must be rejected . Again , it becomes infinite if y = 0 , and this proves to be a solution of the differential equation , the limiting value of the indeterminate function in the ...
... becomes infinite if x = 0 ; but this not involving y must be rejected . Again , it becomes infinite if y = 0 , and this proves to be a solution of the differential equation , the limiting value of the indeterminate function in 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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