A Treatise on Differential Equations. Supplementary Volume |
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Page 23
... factor which the singular solu- tion makes to vanish . If we knew that factor , we could by rejecting it reduce the given differential equation to a form in which it would no longer be satisfied by the singular solution . Now Poisson ...
... factor which the singular solu- tion makes to vanish . If we knew that factor , we could by rejecting it reduce the given differential equation to a form in which it would no longer be satisfied by the singular solution . Now Poisson ...
Page 25
... factor ua from the transformed equation . It has been shewn in the treatment of Clairaut's equation , how in the ascent by differentiation to an equation of a higher order a somewhat analogous effect is produced , the singular solu ...
... factor ua from the transformed equation . It has been shewn in the treatment of Clairaut's equation , how in the ascent by differentiation to an equation of a higher order a somewhat analogous effect is produced , the singular solu ...
Page 29
... factor of the right - hand member of the above equation , does not become infinite . Again , F ( x , u ) − F ( x , 0 ) vanishing when u = 0 , we have u du - = 0 , ( x , u ) when u is made infinitesimal as was to be shewn . It will be ...
... factor of the right - hand member of the above equation , does not become infinite . Again , F ( x , u ) − F ( x , 0 ) vanishing when u = 0 , we have u du - = 0 , ( x , u ) when u is made infinitesimal as was to be shewn . It will be ...
Page 30
... factor which neither vanishes nor becomes infinite when u = 0. If that integral tend to 0 with u the solution is singular . Ex . 1. Determine whether y = 0 is a singular solution or particular integral of the differential equation dy dx ...
... factor which neither vanishes nor becomes infinite when u = 0. If that integral tend to 0 with u the solution is singular . Ex . 1. Determine whether y = 0 is a singular solution or particular integral of the differential equation dy dx ...
Page 31
... factor which neither vanishes nor becomes infinite when y = 0 , x dy = Sylogy log log y log log 0 = log y log log 0 ' and this being infinite , however small y may be , may properly be said to tend to infinity as y tends to 0. The ...
... factor which neither vanishes nor becomes infinite when y = 0 , x dy = Sylogy log log y log log 0 = log y log log 0 ' and this being infinite , however small y may be , may properly be said to tend to infinity as y tends to 0. 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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