A Treatise on Differential Equations |
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Page vi
... applications of deductive reasoning ; but those applications may be only possible through the methods and the processes which belong to an earlier stage . Thus , to take an illustration from the subject of the follow- ing work , the ...
... applications of deductive reasoning ; but those applications may be only possible through the methods and the processes which belong to an earlier stage . Thus , to take an illustration from the subject of the follow- ing work , the ...
Page xii
... application , 82. So- lution of P1dx + P2dy + Q ( xdy − ydx ) = 0,84 . Jacobi's equation , 85 . Euler's method , 86. Exercises , 88 . CHAPTER VI . ON SOME REMARKABLE EQUATIONS OF THE FIRST ORDER 69 du dx Riccati's equation + bu2 = cxm ...
... application , 82. So- lution of P1dx + P2dy + Q ( xdy − ydx ) = 0,84 . Jacobi's equation , 85 . Euler's method , 86. Exercises , 88 . CHAPTER VI . ON SOME REMARKABLE EQUATIONS OF THE FIRST ORDER 69 du dx Riccati's equation + bu2 = cxm ...
Page xiii
... APPLICATIONS 209 238 Curves of Pursuit , Different problems , 239-244 . Trajectories , 245 . 251. Solution of a differential equation , 254. Involutes , 256 . Inverse problem of caustics , 258-263 . Direct problem , 259 . Intrinsic ...
... APPLICATIONS 209 238 Curves of Pursuit , Different problems , 239-244 . Trajectories , 245 . 251. Solution of a differential equation , 254. Involutes , 256 . Inverse problem of caustics , 258-263 . Direct problem , 259 . Intrinsic ...
Page 1
... applications , as well as in its theory and its processes , the primitive relation between the variables x and y is supposed to be known . х In the Integral Calculus , on the other hand , it is the rela- tion among the primitive ...
... applications , as well as in its theory and its processes , the primitive relation between the variables x and y is supposed to be known . х In the Integral Calculus , on the other hand , it is the rela- tion among the primitive ...
Page 8
... application of the former term we contemplate the differential equation as prior in the order of thought , and the explicit relation among the variables as thence deduced by a process of solution ; while in the strict use of the latter ...
... application of the former term we contemplate the differential equation as prior in the order of thought , and the explicit relation among the variables as thence deduced by a process of solution ; while in the strict use of the latter ...
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2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter cloth complete primitive condition Crown 8vo curve deduce determined differential coefficients dp dq dp dy dt dt dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition EDUCATIONAL BOOKS elementary eliminating equa exact differential example expressed fcap finite given equation gives Hence homogeneous functions independent variable integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation problem reduced relation represent respect result satisfied second member second order shew singular solution substituting suppose theorem tion transformation TREATISE whence X₁ Y₁ аф
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