A Treatise on Differential EquationsMacmillan, 1865 - 496 sider |
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Side 16
... contain y in its expression , nor from the satisfying of dy d = ∞ dx dy dc 2ndly . It may be that dp dy when the relation in question does not involve x in its ex- pression . For these conditions being respectively derived from = dx O ...
... contain y in its expression , nor from the satisfying of dy d = ∞ dx dy dc 2ndly . It may be that dp dy when the relation in question does not involve x in its ex- pression . For these conditions being respectively derived from = dx O ...
Side 23
... containing a 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 ...
... containing a 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 ...
Side 41
... containing an additional portion consisting of z , and differential coefficients of z multiplied by known functions of x . The result of substitution of these values in the given differential equation will therefore consist also of two ...
... containing an additional portion consisting of z , and differential coefficients of z multiplied by known functions of x . The result of substitution of these values in the given differential equation will therefore consist also of two ...
Side 48
... contain . A solu- tion containing n - 1 arbitrary constants is called by 48 [ CH . XXIII . ADDITIONS TO CHAPTER X.
... contain . A solu- tion containing n - 1 arbitrary constants is called by 48 [ CH . XXIII . ADDITIONS TO CHAPTER X.
Side 49
George Boole. tion containing n - 1 arbitrary constants is called by him a singular solution of the first order ; one containing n - 2 ar- bitrary constants a singular solution of the second order , and so on . Adopting this language we ...
George Boole. tion containing n - 1 arbitrary constants is called by him a singular solution of the first order ; one containing n - 2 ar- bitrary constants a singular solution of the second order , and so on . Adopting this language we ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
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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