A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Side 28
... illustrate the same doctrine geometrically , if x and y represent rectangular co - ordinates , any system such as the above would represent a series of points of which the abscissæ having been assumed arbitrarily , the corresponding ...
... illustrate the same doctrine geometrically , if x and y represent rectangular co - ordinates , any system such as the above would represent a series of points of which the abscissæ having been assumed arbitrarily , the corresponding ...
Side 41
... y , and an arbitrary constant . The examples of finite solu- tion which have been given above , illustrate this truth . But a further and more complete illustration is afforded by the ART . 12. ] 41 OF THE FIRST ORDER AND DEGREE .
... y , and an arbitrary constant . The examples of finite solu- tion which have been given above , illustrate this truth . But a further and more complete illustration is afforded by the ART . 12. ] 41 OF THE FIRST ORDER AND DEGREE .
Side 123
... illustrates the process but not its advantages . Ex . 2. Given x = 1 + p + p3 . Here dy = pdx = pdp + 3p3dp ; p3 3p⭑ therefore y = + + C ..... 2 4 ( 5 ) , between which and the original equation p must be eliminated . We may do this so ...
... illustrates the process but not its advantages . Ex . 2. Given x = 1 + p + p3 . Here dy = pdx = pdp + 3p3dp ; p3 3p⭑ therefore y = + + C ..... 2 4 ( 5 ) , between which and the original equation p must be eliminated . We may do this so ...
Side 125
... illustrate the process above described . Ex . Given y = xp + · m Ρ Here differentiating we have x ) = 0 m \ dp p * dx From the equation dp = 0 , we have dx p = c , whence y = cx + m the complete primitive . From the equation x p = 8 m 2 ...
... illustrate the process above described . Ex . Given y = xp + · m Ρ Here differentiating we have x ) = 0 m \ dp p * dx From the equation dp = 0 , we have dx p = c , whence y = cx + m the complete primitive . From the equation x p = 8 m 2 ...
Side 137
... illustrate Art . 6 . The singular solutions as well as the complete primitives are to be determined , dy ( dy dx dx - 2 dy 12 . y = x + dx dy 13 . y = = x + - d / { ¿ ' — a ' ( d ) " } ⋅ a2 dx The following examples are in illustration ...
... illustrate Art . 6 . The singular solutions as well as the complete primitives are to be determined , dy ( dy dx dx - 2 dy 12 . y = x + dx dy 13 . y = = x + - d / { ¿ ' — a ' ( d ) " } ⋅ a2 dx The following examples are in illustration ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
2ndly algebraic arbitrary constants arbitrary function assume C₁ C₂ Chap Chapter complete primitive condition Crown 8vo curve deduce derived determined differential coefficients dp dp dp dq dp dy dt dt dv du dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dy dz dz Edition eliminating equa exact differential expressed fcap finite given equation Hence homogeneous functions independent variable integrating factor involving method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral pdx+qdy primitive equation reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation whence X₁ y₁