A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 11
... Substituting it in the com- plete primitive we get y = c , which confirms this . Second . Let y = 0. This satisfies the differential equa- tion ; but from the fact that it comes from d dx = ∞ we have no inference ; from the fact that ...
... Substituting it in the com- plete primitive we get y = c , which confirms this . Second . Let y = 0. This satisfies the differential equa- tion ; but from the fact that it comes from d dx = ∞ we have no inference ; from the fact that ...
Página 22
... substituting in which the proposed solution , we find 2 ( y - xp ) value of dy obtained from the dx 9 day dx2 ( x2 + y2 ) 2 2y3 = - 8 y3 • Now this differing from the value before obtained , we con- clude that the solution is singular ...
... substituting in which the proposed solution , we find 2 ( y - xp ) value of dy obtained from the dx 9 day dx2 ( x2 + y2 ) 2 2y3 = - 8 y3 • Now this differing from the value before obtained , we con- clude that the solution is singular ...
Página 41
... substituting for the value X as above determined . dx stitute as above for dci dx ' We observe that the coefficient of z is here a known function of x . If we differentiate this equation and in the result sub- we shall have a result of ...
... substituting for the value X as above determined . dx stitute as above for dci dx ' We observe that the coefficient of z is here a known function of x . If we differentiate this equation and in the result sub- we shall have a result of ...
Página 51
... substituting and transposing , do dn - 1Sy do dn - 2Sy dr Sy - dx " dyn - 1 dx dyn - 2 dx - 2 - & c . = 0 ...... ( 10 ) . Let us consider the real nature of this equation . If a value of y , suppose y ( x ) , satisfy the given differ ...
... substituting and transposing , do dn - 1Sy do dn - 2Sy dr Sy - dx " dyn - 1 dx dyn - 2 dx - 2 - & c . = 0 ...... ( 10 ) . Let us consider the real nature of this equation . If a value of y , suppose y ( x ) , satisfy the given differ ...
Página 60
... substituting the values of p and q formed from this in the given equation , we have pdw + Q dx dw dw + R = 0 , dy dz which must be identically satisfied . In like manner , u = a , v = b being solutions of the same equation , we find du ...
... substituting the values of p and q formed from this in the given equation , we have pdw + Q dx dw dw + R = 0 , dy dz which must be identically satisfied . In like manner , u = a , v = b being solutions of the same equation , we find du ...
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Términos y frases comunes
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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