A Treatise on Differential EquationsMacmillan, 1865 - 496 σελίδες |
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Σελίδα 25
... appear from the demonstration of the follow- ing theorem , which is in effect Poisson's freed from arbitrary assumptions . 9. PROPOSITION . If u = 0 be a solution of a differential equation of the first order between y and x , and du ...
... appear from the demonstration of the follow- ing theorem , which is in effect Poisson's freed from arbitrary assumptions . 9. PROPOSITION . If u = 0 be a solution of a differential equation of the first order between y and x , and du ...
Σελίδα 31
... appear at first sight as if in the above ex- ample we ought to write log y log log 0 - log 1 = 0 when y is made equal to 0. But the course of the demonstra- tion shews that the value of the definite integral must be first obtained on ...
... appear at first sight as if in the above ex- ample we ought to write log y log log 0 - log 1 = 0 when y is made equal to 0. But the course of the demonstra- tion shews that the value of the definite integral must be first obtained on ...
Σελίδα 32
... appearing in a too isolated form have been neglected , forgotten , and rediscovered . I purpose here to give a brief ... appear to have been led by accident to the noticing of singular solutions ; the former while directly occupied on ...
... appearing in a too isolated form have been neglected , forgotten , and rediscovered . I purpose here to give a brief ... appear to have been led by accident to the noticing of singular solutions ; the former while directly occupied on ...
Σελίδα 34
... appears first to have developed the theory of singular solutions in its two forms of derivation from the complete primitive and derivation from the differen- tial equation , and to have established the essential connexion of these . But ...
... appears first to have developed the theory of singular solutions in its two forms of derivation from the complete primitive and derivation from the differen- tial equation , and to have established the essential connexion of these . But ...
Σελίδα 49
... appear in the expression of the singular solution . Ex . The equation dy , 1 y - x + = x2 · dy d'y dx 2 dx dx 2 ( dy d'y 2 - = = 0 dx dx has for its complete primitive ax2 2 y = + bx + a2 + b2 required its singular solution ...
... appear in the expression of the singular solution . Ex . The equation dy , 1 y - x + = x2 · dy d'y dx 2 dx dx 2 ( dy d'y 2 - = = 0 dx dx has for its complete primitive ax2 2 y = + bx + a2 + b2 required its singular solution ...
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arbitrary constants Cambridge Chap Chapter College complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dF dF dp dF dx dFdF differential coefficients dp dF dp dp dx dp dq dp dy dp₁ dq dp dv dv dx dp dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor function given equation Hence J. P. MAHAFFY Jacobi Last Multiplier linear partial differential m₁ memoir ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole reduced represent result revised School shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence X₁ Y₁ аф
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