A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα ix
... factors , to singular solutions , to the inverse problems of Geometry and Optics , to partial differential equations both of the first and second order , and , as has already been intimated , to symboli- cal methods . The demonstrations ...
... factors , to singular solutions , to the inverse problems of Geometry and Optics , to partial differential equations both of the first and second order , and , as has already been intimated , to symboli- cal methods . The demonstrations ...
Σελίδα xi
... III . EXACT DIFFERENTIAL EQUATIONS OF THE FIRST DEGREE General criterion , 47. Mode of solution , 50. Practical simplifica- tions , 52. Exercises , 53 . 23 47 CHAPTER IV . ON THE INTEGRATING FACTORS OF THE DIFFERENTIAL.
... III . EXACT DIFFERENTIAL EQUATIONS OF THE FIRST DEGREE General criterion , 47. Mode of solution , 50. Practical simplifica- tions , 52. Exercises , 53 . 23 47 CHAPTER IV . ON THE INTEGRATING FACTORS OF THE DIFFERENTIAL.
Σελίδα xii
... FACTORS OF THE EQUATION Mdx + Ndy = 0 Partial differential equation for integrating factors , 69. Solution when the integrating factor is a function of x , 70 - of y , 71 — of xy , 72 . When homogeneous , 74-76 . More general ...
... FACTORS OF THE EQUATION Mdx + Ndy = 0 Partial differential equation for integrating factors , 69. Solution when the integrating factor is a function of x , 70 - of y , 71 — of xy , 72 . When homogeneous , 74-76 . More general ...
Σελίδα 9
... factors , i.e. of factors which do not contain dy , and do not therefore affect dy dx dx ' the relation in which stands to x and y . For it is in that relation , as already intimated , Art . 2 , that the essential character of the ...
... factors , i.e. of factors which do not contain dy , and do not therefore affect dy dx dx ' the relation in which stands to x and y . For it is in that relation , as already intimated , Art . 2 , that the essential character of the ...
Σελίδα 32
... factor . Thus the equation xdx 1+ y - ydy 1 + x = : 0 becomes on multiplying by ( 1 + x ) ( 1 + y ) , - x ( 1 + x ) dx − y ( 1 + y ) dy = .0 , in which the variables are separated . Integration then gives x2 + x3 - y2 - y3 2 3 2 3 = C ...
... factor . Thus the equation xdx 1+ y - ydy 1 + x = : 0 becomes on multiplying by ( 1 + x ) ( 1 + y ) , - x ( 1 + x ) dx − y ( 1 + y ) dy = .0 , in which the variables are separated . Integration then gives x2 + x3 - y2 - y3 2 3 2 3 = C ...
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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