A Treatise on Differential Equations. Supplementary VolumeMacmillan, 1865 - 235 σελίδες |
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Σελίδα 53
... Eliminating there results d'y 2 dy dx2 dy dy + 2x = 0 . dx da from the given equation by means of this dx2 dy 2 a + x - · dx 2 + ∞ ) dy − ( 1 + x2 ) y − 0 , 16 and we find on differentiating this that it does constitute a solution of ...
... Eliminating there results d'y 2 dy dx2 dy dy + 2x = 0 . dx da from the given equation by means of this dx2 dy 2 a + x - · dx 2 + ∞ ) dy − ( 1 + x2 ) y − 0 , 16 and we find on differentiating this that it does constitute a solution of ...
Σελίδα 57
... eliminating dx , dy , from the equations dU du dx + dy = 0 , dy dx dx du dx + du dy = 0 , dy and therefore it is du du du du dx dy dy dx as expressed in Chap . II . = 0 , We proceed to the general demonstration . Let the first member of ...
... eliminating dx , dy , from the equations dU du dx + dy = 0 , dy dx dx du dx + du dy = 0 , dy and therefore it is du du du du dx dy dy dx as expressed in Chap . II . = 0 , We proceed to the general demonstration . Let the first member of ...
Σελίδα 58
... eliminate from that of u , the quantities x ,,,, ... 1 , and so express u as a function of u1 , u ,, ... u and x . Suppose Un - 1 this done , then the system ( 3 ) , ( 4 ) will be converted into du1 = 0 , du , = 0 , ... .. dun - 1 = 0 ...
... eliminate from that of u , the quantities x ,,,, ... 1 , and so express u as a function of u1 , u ,, ... u and x . Suppose Un - 1 this done , then the system ( 3 ) , ( 4 ) will be converted into du1 = 0 , du , = 0 , ... .. dun - 1 = 0 ...
Σελίδα 60
... equation , we find du P dx + Q du + R du = 0 , dy dz dv P dx + Q dy dv + R dv dz = = 0 , which must be identically satisfied . Eliminating P , Q , R from these three equations 60 [ CH . XXIV . ADDITIONS TO CHAPTER XIV .
... equation , we find du P dx + Q du + R du = 0 , dy dz dv P dx + Q dy dv + R dv dz = = 0 , which must be identically satisfied . Eliminating P , Q , R from these three equations 60 [ CH . XXIV . ADDITIONS TO CHAPTER XIV .
Σελίδα 61
George Boole Isaac Todhunter. Eliminating P , Q , R from these three equations , it results that the functional ... eliminating dz , dx , dx ,, ... dx , from du , = 0 , du , = 0 , ...... du2 = 0 , expressed as total differential ...
George Boole Isaac Todhunter. Eliminating P , Q , R from these three equations , it results that the functional ... eliminating dz , dx , dx ,, ... dx , from du , = 0 , du , = 0 , ...... du2 = 0 , expressed as total differential ...
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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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