A Treatise on Differential Equations |
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Page 5
... expression for y [ see Eq . ( 30 ) of Chap . 11. ] in ascending powers of x , we have + 1.2 1.2.3 y = A ̧ + A ̧x + A , x2 A_r in which A ̧ = Σ ƒn ( X , Y ̧ ) ( — x ̧ ) * → 1.2 ... ( nr ) + & c . , ( 32 ) ........ the summation ...
... expression for y [ see Eq . ( 30 ) of Chap . 11. ] in ascending powers of x , we have + 1.2 1.2.3 y = A ̧ + A ̧x + A , x2 A_r in which A ̧ = Σ ƒn ( X , Y ̧ ) ( — x ̧ ) * → 1.2 ... ( nr ) + & c . , ( 32 ) ........ the summation ...
Page 7
... expression of the complete primitive a certain variety of form may be given without affecting its generality in the sense above affirmed . Thus , if to the solutions of the component differential equations we give the forms -ax ує c1 ...
... expression of the complete primitive a certain variety of form may be given without affecting its generality in the sense above affirmed . Thus , if to the solutions of the component differential equations we give the forms -ax ує c1 ...
Page 11
... expression , nothing is to be inferred whether it is singular or not . Then the proper test is d = ∞ · dac In this example we have dp = ∞ gives " o ; no inference ; dy d = ∞ gives x ( +1 ) y ̄1 = ∞ . -1 dx - Hence x = 0 , provided n ...
... expression , nothing is to be inferred whether it is singular or not . Then the proper test is d = ∞ · dac In this example we have dp = ∞ gives " o ; no inference ; dy d = ∞ gives x ( +1 ) y ̄1 = ∞ . -1 dx - Hence x = 0 , provided n ...
Page 13
... expression . Of the partial tests do аф do = 0 , = ∞ = ∞ dc dx dy the first is not satisfied , the last two are satisfied . The determination of c as a function of x by the solution of the equation df ( a , c ) = 0 is equivalent to ...
... expression . Of the partial tests do аф do = 0 , = ∞ = ∞ dc dx dy the first is not satisfied , the last two are satisfied . The determination of c as a function of x by the solution of the equation df ( a , c ) = 0 is equivalent to ...
Page 16
... 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 and dc in their ...
... 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 and dc in their ...
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Common terms and phrases
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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