A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα xii
... INTEGRATING 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 ...
... INTEGRATING 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 ...
Σελίδα 35
... factor x " , ☀ ( 2 ) dx + 4 ( 2 ) dy = 0 $ Now assuming y = vx , we have y ... integrating log x + √ √ ( v ) + v ¥ ( v ) = C ............... ( 18 ) . It ... integrate the equation { x − √√ ( xy ) — y } dx + √ ( xy ) dy = 0 , -- by ...
... factor x " , ☀ ( 2 ) dx + 4 ( 2 ) dy = 0 $ Now assuming y = vx , we have y ... integrating log x + √ √ ( v ) + v ¥ ( v ) = C ............... ( 18 ) . It ... integrate the equation { x − √√ ( xy ) — y } dx + √ ( xy ) dy = 0 , -- by ...
Σελίδα 55
George Boole. CHAPTER IV . -0 . ON THE INTEGRATING FACTORS OF THE DIFFERENTIAL EQUATION Mdx + Ndy = 0 . 1. THE first member of the equation Mdx + Ndy = 0 not being necessarily an exact differential , analysts have sought to render it ...
George Boole. CHAPTER IV . -0 . ON THE INTEGRATING FACTORS OF THE DIFFERENTIAL EQUATION Mdx + Ndy = 0 . 1. THE first member of the equation Mdx + Ndy = 0 not being necessarily an exact differential , analysts have sought to render it ...
Σελίδα 56
... integrating factors , all of which are included under a single functional expression . It has been shewn , Chap . II ... factor μ . 3. The form of the complete primitive is however without 56 [ CH . IV . ON THE INTEGRATING FACTORS .
... integrating factors , all of which are included under a single functional expression . It has been shewn , Chap . II ... factor μ . 3. The form of the complete primitive is however without 56 [ CH . IV . ON THE INTEGRATING FACTORS .
Σελίδα 57
... integrating factor , a special deter- mination of which has already been given , Art . 1 . To investigate the general form under which all such special determinations are included , let us suppose μ to be a particular integrating factor ...
... integrating factor , a special deter- mination of which has already been given , Art . 1 . To investigate the general form under which all such special determinations are included , let us suppose μ to be a particular integrating factor ...
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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