A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα 8
... deduced by a process of solution ; while in the strict use of the latter term the order both of thought and of process is reversed . Genesis of Differential Equations . 6. The theory of the genesis of differential equations from their ...
... deduced by a process of solution ; while in the strict use of the latter term the order both of thought and of process is reversed . Genesis of Differential Equations . 6. The theory of the genesis of differential equations from their ...
Σελίδα 19
... such limitation . Monge has deduced the general differential equation of lines of the second order expressed by the algebraic equation ax2 + bxy + cy2 + ex + fy = 1 . It is 3 9 ( de ) d'y - 45 2-2 ART . 11. ] 19 GEOMETRICAL ILLUSTRATIONS .
... such limitation . Monge has deduced the general differential equation of lines of the second order expressed by the algebraic equation ax2 + bxy + cy2 + ex + fy = 1 . It is 3 9 ( de ) d'y - 45 2-2 ART . 11. ] 19 GEOMETRICAL ILLUSTRATIONS .
Σελίδα 22
... deduce 1st the differential equations of the first order involving a and b as their respective arbitrary constants ; 2dly the general functional expression for all differential equa- tions of the first order derivable from the same ...
... deduce 1st the differential equations of the first order involving a and b as their respective arbitrary constants ; 2dly the general functional expression for all differential equa- tions of the first order derivable from the same ...
Σελίδα 24
... deduce its general solution in a series . PROP . 1. Let V and v be explicit functions of the two vari- ables x and y . Then , if V be expressible as a function of v , the condition dV dv dV dv dx dy dy dx = 0 ........ ( 1 ) will be ...
... deduce its general solution in a series . PROP . 1. Let V and v be explicit functions of the two vari- ables x and y . Then , if V be expressible as a function of v , the condition dV dv dV dv dx dy dy dx = 0 ........ ( 1 ) will be ...
Σελίδα 45
... deduce by that dx dy - method the solution of the equation - ay = x + 1 . x Ax 6. Integrate , by the direct application of ( 23 ) , the linear equations , x 1 24 + 1 + 202 = 20 ( 1 + 205 ) y 2x x2 ) ( 1 ) dy dx dy ( 2 ) x ( 1 − x3 ) dy ...
... deduce by that dx dy - method the solution of the equation - ay = x + 1 . x Ax 6. Integrate , by the direct application of ( 23 ) , the linear equations , x 1 24 + 1 + 202 = 20 ( 1 + 205 ) y 2x x2 ) ( 1 ) dy dx dy ( 2 ) x ( 1 − x3 ) dy ...
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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